There
is a general awareness that contemporary physics has brought about an
important revision in man’s conception of the universe and his relation to
it.The suggestion has been
made that this revision pierces to
the basis of man’s fate and freedom, affecting even his conception
of his capacity to control his own destiny.In no portion of physics does this suggestion show itself more
pointedly than in the principle of indeterminacy of quantum mechanics.The author of this book is the discoverer of this principle.In fact, it usually bears his name.Hence, no one is more competent to pass judgment on what it means
than he.

In
his previous book, The Physical Principles of the Quantum Theory (1930),
Heisenberg gave an exposition of the theoretical interpretation,
experimental meaning and mathematical apparatus of quantum mechanics for
professional physicists.Here
he pursues this and other physical theories with respect to their
philosophical implications and some of their likely social consequences for the layman.More
specifically, he attempts here to raise and suggest answers to three
questions: (1) What do the
experimentally verified theories of contemporary physics affirm?(2) How do they permit or require man to think of himself in
relation to his universe?(3)
How is this new way or thinking,
which is the creation of the modem West, going to affect other parts of the
world?

The
third of these questions is dealt with briefly by Heisenberg
at the beginning and end of this inquiry.The brevity of his remarks should not lead the reader to pass
lightly over their import.As he notes,
whether we like it or not, modem ways are going to alter and in part
destroy traditional customs and values.It is frequently assumed by native leaders of nonWestern societies,
and also often by their Western advisers, that the problem of introducing modem scientific instruments and ways
into Asia, the Middle East and Africa is merely that of giving the native
people their political independence and then providing them with the
funds and the practical instruments.This facile assumption overlooks several things.First, the instruments of modem science derive from its theory and
require a comprehension of that theory for their correct manufacture or
effective use.Second, this
theory in turn rests on philosophical, as well as physical, assumptions.When comprehended, these philosophical assumptions generate a
personal and social mentality and behavior quite different from, and at
points incompatible with, the family, caste and tribally centered mentality
and values of the native Asian, Middle Eastern or African people.In short, one cannot bring in the instruments of modern physics
without sooner or later introducing its philosophical mentality, and this
mentality, as it captures the scientifically trained youth, upsets the old
familial and tribal moral loyalties.If
unnecessary emotional conflict and social demoralization are not to result,
it is important that the youth understand what is happening to them.This means that they must see their experience as the coming together
of two different philosophical mentalities,
that of their traditional culture and that of the new physics.Hence, the importance for everyone of understanding the philosophy of
the new physics.

But
it may be asked, Isn’t physics quite independent of philosophy?Hasn’t modem physics become effective only by dropping
philosophy?Clearly, Heisenberg
answers both of these questions in the negative.Why is this the case?Newton
left the impression that there were no assumptions in his physics which were
not necessitated by the experimental data.This occurred when he suggested that he made no hypotheses and that
he had deduced his basic concepts and laws from the experimental
findings.Were this conception
of the relation between the
physicist’s experimental observations and his theory correct, Newton’s theory would never have required modifica­tion, nor
could it ever have implied consequences which experiment does not confirm.Being implied by the facts, it would be as indubitable and final as
they are.

In
1887, however, an experiment performed by Michelson and Morley revealed a
fact which should not exist were the theoretical assumptions of Newton the
whole truth.This made it
evident that the relation between the physicist’s experimental facts and
his theoretical assumptions is quite other than what Newton had led many
modem physicists to suppose.When,
some ten years later, experiments on radiation from black bodies
enforced an additional reconstruction in Newton’s way of thinking about
his subject matter, this conclusion became inescapable.Expressed positively, this means that the theory of physics is
neither a mere description of experimental facts nor something deducible
from such a description; instead, as Einstein has emphasized, the physical
scientist only arrives at his theory by speculative
means.The deduction in his
method runs not from facts to the assumptions of the theory but from the
assumed theory to the facts
and the experimental data.Consequently,
theories have to be proposed speculatively and pursued deductively with
respect to their many consequences so that they can be put to indirect
experimental tests.In short,
any theory of physics makes more physical and philosophical
assumptions than the facts alone give or imply.For this reason, any theory is sub­ject to further modification and
reconstruction with the advent of new evidence that is incompatible, after
the manner of the results of the Michelson-Morley experiment, with its basic
assumptions.

These
assumptions, moreover, are philosophical in character.They may be ontological, ie. referring to the subject matter of
scientific knowledge which is independent of its relation to the perceiver;
or they may be epistemological, ie. referring to the relation of the
scientist as experimenter and knower to the subject matter which he knows.Einstein’s special and general theories of relativity modify the
philosophy of modem physics in the first of these two respects by radically
altering the philosophical theory of space and time and their relation to
matter.Quantum mechanics,
especially its Heisenberg principle of indeterminacy, has been notable for
the change it has brought in the physicist’s epistemological theory of the
relation of the experimenter to the object of his scientific knowledge.Perhaps the most novel and important thesis of this book is its
author’s contention that quantum mechanics has brought the concept of
potentiality back into physical science.This makes quantum theory as important for ontology as for
epistemology.At this point,
Heisenberg’s philosophy of physics has an element in common with that of
Whitehead.

It
is because of this introduction of potentiality into the subject matter of physics, as distinct from the epistemological predicament
of physicists, that Einstein objected to quantum mechanics.He expressed this objection by saying: “God does not play dice.”
The point of this statement is that the game of dice rests on the laws of
chance, and Einstein believed that the latter concept finds its scientific
meaning solely in the epistemological limitations of the finite knowing mind
in its relation to the omnicomplete object of scientific knowledge and,
hence, is misapplied when referred ontologically to that object itself.The object being per se all
complete and in this sense omniscient, after the manner of God, the concept
of chance or of probability is inappropriate for any scientific description
of it.

This
book is important because it contains Heisenberg’s answer to this criticism of his principle of indeterminacy and of
quantum theory by Einstein and by others.In understanding this answer two things must be kept in mind: (1) The
aforementioned relation between the
data of experimental physics
and the concepts of its theory.(2)
The difference between the role of the concept of probability in (a)
Newton’s mechanics and Einstein’s theory of relativity and in (b) quantum
mechanics.Upon (1), Einstein and Heisenberg, and rela­tivistic
mechanics and quantum mechanics, are in agreement.

It
is only with respect to (2) that they differ.Yet the reason for Heisenberg’s
and the quantum physicist’s difference from Einstein on (2) depends in considerable part on (1) which Einstein admits.(1) affirms that the experimental data of physics do not imply its
theoretical concepts.From this
it follows that the object of scientific knowledge is never known directly
by observation or experimentation, but is only known by speculatively
proposed theoretic construction or axiomatic postulation, tested only

indirectly and experimentally via its deduced consequences.To with the same initial
conditions must be repeated many times, and the values of position or
momentum, which may be different in each observation, must similarly be
found to be distributed according to the predicted probability distribution.In short, the crucial difference between quantum mechanics and
Einstein’s or Newton’s mechanics centers in the definition of a
mechanical system at any moment of time, and this difference is that quantum
mechanics introduces the concept of probability into its definition of state
and the mechanics of Newton and Einstein does not.

This
does not mean that probability had no place in Newton’s or Einstein’s
mechanics.Its place was,
however, solely in the theory of errors by means of which the accuracy of
the Yes or No verification or
nonconfirmation of the prediction of the theory was determined.Hence, the concept of probability and chance was restricted to the
epistemological relation of the scientist in the verification of what he
knows; it did not enter into the theoretical statement of what he knows.Thus, Einstein’s dictum that “God does not play dice” was
satisfied in his two theories of
relativity and in Newton’s mechanics.

Is
there any way of deciding between Einstein’s contention and that of
Heisenberg and other quantum theorists?Many answers have been given to this question.Some physicists and philosophers, emphasizing operational
definitions, have argued that, since all physical theories, even classical
ones, entail human error and uncertainties, there is nothing to be decided
between Einstein and the quantum theorists.This, however, is (a) to overlook the presence of axiomatically
constructed, constitutive theoretic definitions as well as theory-of-errors,
operational definitions in scientific method and (b) to suppose that the
concept of probability and the even more complex uncertainty find the object
of scientific knowledge we must go, therefore, to
its theoretical assumptions.

When
we do this for (a) Newton’s or Einstein’s mechanics and for (b) quantum
mechanics, we discover that the concept of probability or chance enters into
the definition of the state of a physical system, and, in this sense, into
its subject matter, in quantum mechanics, but does not do so in Newton’s
mechanics or Einstein’s theory of relativity.This undoubtedly is what Heisenberg means when he writes in this book
that quantum theory has brought the
concept of potentiality back into physical science.It is also, without question, what Einstein has in mind when
he objects to quantum theory.

Put
more concretely, this difference between quantum mechanics and
previous physical theories may be expressed as follows: In Newton’s and
Einstein’s theory, the state of any isolated mechanical system at a given
moment of time is given precisely when only numbers specifying the position
and momentum of each mass in the system are empirically determined at that
moment of time; no numbers referring to a probability are present.In quantum mechanics the interpretation of an observation of a
system is a rather complicated procedure.The observation may consist in a single reading, the accuracy of
which has to be discussed, or it may comprise a complicated set of data,
such as the photograph of the water droplets in a cloud chamber; in any
case, the result can be stated only in terms of a probability distribution
concerning, for instance, the position or momentum of the particles of the
system.The theory then
predicts the probability distribution for a future time.The theory is not experimentally verified when that future state arrives if merely the
momentum or position numbers in a particular observation lie within the
predicted range.The same
experiment relation enter into quantum mechanics only in the
operational-definitional sense.Heisenberg
shows that the latter supposition is false.

Other
scientists and philosophers, going to the opposite extreme, have argued
that, merely because there is uncertainty in predicting certain phenomena,
this constitutes no argument whatever for the thesis that these phenomena
are not completely determined.This argument combines the statical problem of defining the state’
of a mechanical system at a given time with the dynamical or causal problem
of predicting changes in the state of the system through time.But the concept of probability in quantum theory enters only into its
statics, ie. its theoretical definition of state.The reader will find it wise, therefore, to keep distinct
these two components, ie. the statical theoretical definition-of-state
component and the dynamic, or causal, theoretical
change-of-state-through-time component.With respect to the former, the concept of probability and the
attendant uncertainty enter theoretically and in principle; they do not
refer merely to the operational and epistemological uncertainties and
errors, arising from the finiteness of, and inaccuracies in, human behavior,
that are common to any scientific theory and any experimentation whatsoever.

But,
why, it may be asked, should the concept of probability be introduced into
the theoretic definition of the state of a mechanical system at any
statical moment in principle?In
making such a theoretical construct by axiomatic postulation, do not
Heisenberg and quantum theoreticians generally beg the question at issue
between themselves and Einstein?This
book makes it clear that the answer to these questions is as follows: The reason
for the procedure of quantum mechanics is thesis (1) above, which Einstein
himself also accepts.

Thesis
(1) is that we know the object of scientific knowledge only by the
speculative means of axiomatic theoretic construction or postulation;
Newton’s suggestion that the physicist can deduce our theoretical concepts
from the experimental data being false.It follows that there is no a priori or empirical meaning for
affirming that the object of scientific knowledge, or, more specifically,
the state of a mechanical system at a given time t1, must be defined
in a particular way.The sole
criterion is, which set of theoretic assumptions concerning the subject
matter of mechanics when pursued to their deduced experimental consequences
is confirmed by the experimental data?

Now,
it happens that when we theoretically and in principle define
the state of a mechanical system for subatomic phenomena in terms solely of
numbers referring to position and momentum, as Einstein would have us do,
and deduce the consequences for radiation from black bodies, this
theoretical assumption concerning the state of a mechanical system and the subject
matter of atomic physics is shown to be false by experimental evidence.The experimental facts simply are not what the theory calls for.When, however, the traditional theory is modified with the
introduction of Planck’s constant and the addition in principle of the
second set of numbers referring to the probability
that the attached position-momentum numbers will be found,
from which the uncertainty principle follows, the experimental data confirm
the new theoretical concepts and principles. In
short, the situation in quantum mechanics with respect to experiments on
black-body radiation is identical with that faced by Einstein with respect
to the Michelson-Morley experiment.In
both cases, only by introducing the new theoretical assumption in
principle is physical theory brought into accord with the experimental
facts.Thus, to assert that,
notwithstanding quantum mechanics,
the positions and momenta of subatomic masses are “really” sharply
located in space and time as designated by one pair of numbers only
and, hence, completely deterministic causally, as Einstein and the
aforementioned philosophers of science would have one do, is to affirm a
theory concerning the subject matter of physical knowledge which experiments
on black-body radiation have shown to be false in the sense that a deductive
experimental consequence of this theory is not confined.

It
does not follow, of course, that some new theory compatible with the foregoing experimental facts might not be discovered in which
the concept of probability does not enter in principle into its definition
of state.Professor Norbert
Wiener, for example, believes that he has clues to the direction such a
theory might take.It would,
however, have to reject a definition of state in terms of the four
space-time dimensions of Einstein’s theory and would, therefore, be
incompatible with Einstein’s thesis on other grounds.Certainly, one cannot rule out such a possibility.Nevertheless, until such an alternative theory is presented, anyone,
who does not claim to possess some a priori or
private source of information concerning what the object of
scientific knowledge must be, has no alternative but to accept the
definition of state of quantum theory and to affirm with the author of this
book that it restores the concept of potentiality to the object of modern
scientific knowledge.Experiments
on black-body radiation require one to conclude that God plays dice.

What
of the status of causality and determinism in quantum mechanics?Probably the interest of the layman and the humanist in this book
depends most on its answer to this question. If this answer is to be
understood, the reader must pay particular attention to Heisenberg’s
description of (a) the aforementioned definition of state by recourse to the
concept of probability and (b) the Schrödinger time-equation.The reader must also make sure, and this is the most difficult task
of all, that the meaning of the words “causality” and “determinism”
in his mind when he asks the above question is identical with the meaning
these words have in Heisenberg’s mind when he specifies the answer.Otherwise, Heisenberg will be answering a different question from the
one the reader is asking and a complete misunderstanding upon the reader’s
part will occur.

The
situation is further complicated by the fact that modem physics permits the
concept of causality to have two different, scientifically precise meanings,
the one stronger than the other, and there is no agreement among physicists
about which one of these two meanings the word “causality” is to be used
to designate.Hence, some
physicists and philosophers of science use the word to designate the
stronger of the two meanings.There
is evidence, at times at least, that
this is Professor Heisenberg’s usage in this book.Other physicists and philosophers, including the writer of
this Introduction, use the word “causality” to designate the weaker of
the two meanings and the word “determinism” to designate the stronger
meaning.When the former usage is followed, the words “causality” and “determinism” become
synonymous.When the second
usage is followed, every deterministic system is a causal system, but not
every causal system is
deterministic.

Great
confusion has entered into previous discussion of this topic because
frequently neither the person who asks the question nor the physicist who
has answered it has been careful to specify in either question or answer
whether he is using the word “causality”
in its weaker or in its stronger modem scientific meaning.If one asks “Does causality hold in quantum mechanics?”
not specifying whether one is asking about causality in its stronger or in
its weaker sense, one then gets apparently contradictory answers from
equally competent physicists.One
physicist, taking the word “causality” in its stronger sense, quite
correctly answers “No.” The other physicist, taking “causality” in
its weaker sense, equally correctly answers “Yes.” Naturally, the
impression has arisen that quantum mechanics is not specific about what the
answer is.Nevertheless, this
impression is erroneous.The answer of quantum mechanics becomes unequivocal the moment
one makes the question and the answer unambiguous by specifying which
meaning of “causality” one is talking about. It is important,
therefore, to become clear about different possible meanings of the word
“causality.” Let us begin with the layman’s
commonsense usage of the word “cause” and then move to the more
exact meanings in modern physics, considering the
meaning in Aristotle’s physics on the way.

One
may say “The stone hit the window and caused the glass to break.” In
this use of “causality” it is thought of as a relation between objects,
ie. between the stone and the windowpane.The scientist expresses the same thing in a different way.He describes the foregoing set of events in terms of the state of the
stone and the windowpane at the earlier time t1 when the stone and the
windowpane were separated and the state of this same system of two objects
at the later time e when the stone and the windowpane
collided.Consequently, whereas the layman tends to
think of causality as a relation between objects, the scientist thinks of it
as a relation between different states of the same object or the same system
of objects at different times.

This is why, in order
to determine what quantum mechanics says about causality, one must
pay attention to two things: (1) The state-function which defines the state
of any physical system at any specific time t.(2) The Schrödinger time-equation which relates the state of the
physical system at the earlier time t1 to its different state at any
specifiable later time t2.What
Heisenberg says about (1) and (2) must, therefore, be read with meticulous
care.

It
will help to understand what quantum mechanics says about the relation between the states of a given physical object, or
system of physical objects, at different times if we consider the possible
properties that this relation might have.The weakest possible case would be that of mere temporal succession
with no necessary connection whatever and with not even a probability,
however small, that the specifiable initial state will be followed in time
by a specifiable future state.Hume
gives us reasons for believing that
the relation between the sensed states of im­mediately
sensed natural phenomena is of this character.Certainly, as he
pointed out, one does not sense any relation of necessary connection.Nor does one directly sense probability.All that sensation gives us with respect to the successive states of
any phenomenon is the mere relation of temporal succession.

This
point is of great importance.It means that one can arrive at a causal theory in any
science or in commonsense knowledge, or even at a probability theory, of the
relation between the successive states of any object or system, only by
speculative means and axiomatically constructed, deductively formulated
scientific and philosophical theory which is tested not directly against the
sensed and experimental data but only indirectly by way of its deductive
consequences.

A
second possibility with respect to the character of the relation
between the states of any physical system at different times is that
the relation is a necessary one, but that one can know what this necessary
connection is only by knowing the future state.The latter knowledge of the future state may be obtained either
by waiting until it arrives or by having seen the future or final state of
similar systems in the past.When
such is the case, causality is teleological.Changes of the system with time are determined by the final
state or goal of the system.The
physical system which is an acorn in the earlier state e and an oak tree in
the later state e is an example.The
connection between these two states seems to be a necessary one.Acorns never change into maple trees or into elephants.They change only into oaks.Yet, given the properties of this physical system in the acorn state
of the earlier time t1, no scientist has as yet been able to deduce the
properties of the oak tree which the system will have at the later time t2.Aristotelian physics affirmed that all causal relations are
teleological.

Another
possibility is that the relation between the states of any
object, or any system of objects, at different times is a relation of
necessary connection such that, given knowledge of the initial state of the
system, assuming isolation, its future state can be deduced.Stated in more technical mathematical language, this means that there
exists an indirectly verified, axiomatically constructed theory whose
postulates (1) specify a state-function, the independent variables of which
completely define the state of the system at any specific instant of time,
and (2) provide a time-equation relating the numerical empirical values of
the independent variables of this function at any earlier time
t1 to their numerical empirical values at any specific later time e
in such a way that by introducing the operationally determined e set of
numbers into the time-equation the future e numbers can be deduced by merely
solving the equation.When this
is the case, the temporal relation between states is said to exemplify
mechanical causation.

It
is to be noted that this definition of mechanical causality leaves open the
question of what independent variables are required
to define the state of the system at any given time.Hence, at least two possibilities arise: (a) the
concept of probability may be used to define the state of the system or (b)
it may not be so used.When (b)
is the case no independent variables referring to probabilities appear in
the state-function and the stronger type of mechanical causality is present.When (a) is the case independent variables referring to
probabilities, as well as to other properties such as position and momentum,
appear in the state-function and only the weaker type of mechanical
causation occurs.If the reader
keeps these two meanings of mechanical
causation in mind and makes sure which meaning Heisenberg is referring to in any particular sentence of this book, he
should be able to get its answer to the question concerning the
status of causality in modem physics.

What
of determinism?Again, there is
no agreed-upon convention among physicists and philosophers of science about
how this word is.to be used.It is in accord with the commonsense usage to identify it with the
strongest possible causality.Let us, then, use the word “determinism” to denote
only the stronger type of mechanical
causation.Then I believe the
careful reader of this book will get the following answer to his question:
In Newtonian, Relativistic and quantum mechanics, mechanical, rather
than teleological, causality holds.This
is why quantum physics is called
quantum mechanics, rather than quantum teleologies.But, whereas causality in Newton’s and Einstein’s physics is of
the stronger type and, hence, both mechanical and deterministic, in quantum
mechanics it is of the weaker causal type and, hence, mechanical but not
deterministic.From the latter
fact it follows that if anywhere in this book Heisenberg uses
the words “mechanical causality” in their stronger, deterministic
meaning and the question be asked “Does mechanical
causation in this stronger meaning hold in quantum mechanics?” then
the answer has to be “No.”

The
situation is even more complicated, as the reader will find,
than even these introductory distinctions between the different
types of causation indicate.It
is to be hoped, however, that this focusing of attention upon these
different meanings will enable the reader to find his way through this
exceptionally important book more
easily than would otherwise be the case.

These distinctions should suffice, also, to enable one to
grasp the tremendous philosophical significance of the introduction of the
weaker type of mechanical causation into modern physics, which has occurred
in quantum mechanics.Its
significance consists in reconciling the concept of objective, and in this
sense ontological, potentiality of Aristotelian physics with the concept of
mechanical causation of modern physics.

It
would be an error, therefore, if the reader, from Heisenberg’s emphasis
upon the presence in quantum mechanics of something analogous to
Aristotle’s concept of potentiality, concluded that contemporary physics
has taken us back to Aristotle’s physics and ontology.It would be an equal error conversely to conclude, because mechanical
causation in its weaker meaning still holds in quantum mechanics, that all is the same now in
modern physics with respect to its causality and ontology as
was the case before quantum mechanics came into being.What has occurred is
that in quantum theory contemporary man
has moved on beyond the classical medieval and the modem world to a
new physics and philosophy which combines consistently some of the basic
causal and ontological assumptions of each.Here, let it be recalled, we use the word “ontological” to denote
any experimentally verified concept of scientific theory which refers to the
object of scientific knowledge rather than merely to the epistemological
relation of the scientist as knower to the object which he knows.Such an experimentally verified philosophical synthesis of
ontological potentiality with ontological mechanical causality, in the
weaker meaning of the latter concept, occurred when physicists found it
impossible to account theoretically for the Compton effect and the results
of experiment on black-body radiation unless they extended the concept of
probability from its Newtonian and Relativistic merely epistemological,
theory-of-errors role in specifying when their theory is or is not
experimentally confirmed to the ontological role, specified in principle in
the theory’s postulates, of characterizing the object of scientific
knowledge itself.

Need
one wonder that Heisenberg went through the subjective emotional
experiences described in this book before he became reconciled to the
necessity, imposed by both experimental and mathematical considerations, of
modifying the philosophical and scientific beliefs of both medieval and
modem man in so deep-going a manner.Those
interested in a firsthand description
of the human spirit in one of its most creative moments
will want to read this book because of this factor alone.The courage which it took to make this step away from the unqualified
determinism of classical modem physics may be appreciated if one recalls
that even such a daring, creative spirit as Einstein balked.He could not allow God to play dice; there could not be potentiality
in the object of scientific knowledge, as the weaker form of mechanical
causality in quantum mechanics allows.

Before
one concludes, however, that God has become a complete gambler and that
potentiality is in all objects, certain limitations which quantum mechanics
places on the application of its weaker form of mechanical causation must be noted.To appreciate these qualifications the reader must note what
this book says about (1) the Compton effect, (2) Planck’s constant h, and
(3) the uncertainty principle which is defined in terms of Planck’s
constant.

This
constant h is a number referring to the quantum of action of any object or
system of objects.This
quantum, which extends atomicity from
matter and electricity to light and even to energy itself, is very small.When the quantum numbers of the system being observed are small, as
is the case with subatomic phenomena, then the uncertainty specified by the
Heisenberg uncertainty principle of the positions and momenta of the
masses of the system becomes
significant.Then, also, the
probability numbers associated with the position-momentum numbers in
the state-function become
significant.When, however, the
quantum numbers of the system are large, then the quantitative amount
of uncertainty specified by the Heisenberg principle becomes insignificant
and the probability numbers in the state-function can be neglected.Such is the case with gross commonsense objects.At this point quantum mechanics with its basically weaker type of
causality gives rise, as a special case of itself, to Newtonian and
relativistic mechanics with their stronger type of causality and
determinism.Consequently, for
human beings considered merely as gross commonsense objects the stronger
type of causality holds and, hence, determinism reigns also.

Nevertheless,
subatomic phenomena are scientifically significant in man.To this extent, at least, the causality governing him is
of the weaker type, and he embodies both mechanical fate and potentiality.There are scientific reasons for believing that this occurs
even in heredity.Any reader
who wants to pursue this topic beyond the pages of this book should turn to What Is Life?by Professor Erwin
Schrödinger, the physicist after whom the time-equation in quantum
mechanics is named.Undoubtedly,
potentiality and the weaker form of causality hold also for countless other
characteristics of human beings, particularly for those cortical neural
phenomena in man that are the epistemic correlates of directly introspected
human ideas and purposes.

If
the latter possibility is the case, the solution of a baffling scientific,
philosophical and even moral problem may be at hand.This problem is: How is the mechanical causation, even in
its weaker form, of quantum mechanics to be reconciled with the
teleological causation patently present in the moral, political and legal
purposes of man and in the teleological causal determination of his bodily
behavior, in part at least, by these purposes?In short, how is the philosophy of physics expounded in this book by Heisenberg to be reconciled with moral, political and legal
science and philosophy?

It
may help the reader to appreciate why this book must be mastered before
these larger questions can be correctly understood or effectively answered
if very brief reference is made here to some articles which relate its
theory of physical causation to the wider relation between mechanism and teleology in the humanities
and the social sciences.The
relevant articles are (a) by
Professors Rosenblueth, Wiener and Bigelow in the journal of The
Philosophy of Science for January, 1943; (b) by Doctors McCulloch
and Pitts in The Bulletin of Mathematical Biophysics, Volume 5, 1943, and Volume 9, 1947; and (c) ‘Chapter XIX
of Ideological Differences and World Order, edited by the writer of this
Introduction and published by the Yale University.University Press, Cambridge; Macmillan Company, New York;
1946.

If
read after this book, (a) will show how teleological causality arises as a
special case of the mechanical causality described by Heisenberg here.Similarly, (b) will provide a physical theory of the neurological
correlates of introspected ideas, expressed in terms of the teleological
mechanical causality of (a), thereby giving an explanation of how ideas can
have a causally significant effect on the behavior of men.Likewise, (c) will show how
the ideas and purposes of moral, political
and legal man relate, by way of (b) and (a), to the theory of
physical potentiality and mechanical causality so thoroughly described by
Heisenberg in this book.

It
remains to call attention to what Professor Heisenberg says about Bohr’s
principle of complementary.This
principle plays a great role in the interpretation of quantum theory by
“the Copenhagen School” to which Bohr and Heisenberg belong.Some students of quantum mechanics, such as Margenau in his book The
Nature of Physical Reality,* are inclined to the conclusion
that quantum mechanics requires merely its definition of state, its
Schrödinger time-equation and those other of its mathematical postulates
which suffice to ensure, as noted above, that Relativistic and Newtonian
mechanics come out of quantum mechanics as one of its special cases.According to the latter
thesis, the principle of complementary arises from the failure to keep the
stronger and weaker form of mechanical causality continuously in mind, with
the resultant attribution of the
stronger form to those portions of quantum mechanics where only
the weaker form is involved.When
this happens, the principle of
complementary has to be introduced to avoid contradiction.If, however, one avoids the foregoing practice, the principle
of complementary becomes, if not unnecessary, at least of a form such that
one avoids the danger, noted by Margenau and appreciated by Bohr, of giving
pseudo solutions to physical and philosophical problems by playing fast and
loose with the law of contradiction, in the name of the principle of
complementary.

By
its use the qualifications that had to be put on both the particle-picture commonsense language of atomic physics and its
commonsense wave-picture language were brought together.But once having formulated the result with axiomatically constructed
mathematical exactitude, any further use of it is merely a superficial
convenience when, leaving aside the exact and
essential mathematical assumptions of quantum mechanics, one indulges
in the commonsense language and images of waves and particles.It has been necessary to go into the different interpretations of the
principle of complementary in order to enable the reader to pass an informed
judgment concerning what Heisenberg says in this book about the commonsense
and Cartesian concepts of material and mental substances.This is the case because his conclusion concerning Descartes
results from his generalization of the principle of complementary beyond
physics, first, to the relation between commonsense biological concepts and
mathematical physical concepts and, second, to the body-mind problem.The
result of this generalization
is that the Cartesian theory of
mental substances comes off
very much better in this
book, as does the concept of substance generally, than is the case in any
other book on the philosophy of contemporary
physics which this writer knows.Whitehead,
for example, concluded that contemporary science
and philosophy find no place for, and have no need of, the concept of
substance.Neutral monists such
as Lord Russell and logical positivists such as Professor Carnap agree.

Generally
speaking, Heisenberg argues that there is no compelling reason to throwaway
any of the commonsense concepts of either biology or mathematical physics,
after one knows the refined concepts that lead to the complete clarification
of the problems in atomic physics.Because
the latter clarification is complete, it is relevant only to a very limited
range of problems within science and cannot enable us to avoid using many
concepts at other places that would not stand critical analysis of the type
carried out in quantum theory.Since
the ideal of complete clarification cannot be achieved—and it is important
that we should not be deceived about this point one may indulge in
the usage of commonsense concepts if it is done with sufficient care and
caution.In this respect,
certainly, complementary is a very useful scientific concept.

In
any event, two things seem clear and make what Heisenberg
says on these matters exceedingly important.First, the principle of complementary and the present validity of the
Cartesian and commonsense concepts of body and mind stand and fall
together.Second, it may be that both these notions are merely
convenient stepladders which should now be, or must eventually be, thrown
away.Even so, in the case of
the theory of mind at least, the stepladder will have to remain until by its
use we find the more linguistically
exact and empirically satis­factory theory that will permit us to
throw the Cartesian language away.To
be sure, piecemeal theories of mind which do not
appeal to the notion of substance now exist, but none of their
authors, unless it be Whitehead, has shown how the language of this
piecemeal theory can be brought into commensurate and compatible
relationship with the scientific language of the other facts of human
knowledge.It is likely, therefore, that anyone, whether he be a
professional physicist or philosopher or the lay reader, who may think he
knows better than Heisenberg on these important matters, runs the grave risk
of supposing he has a scientific theory of mind in its relation to body,
when in fact this is not the case.

Up
to this point we have directed attention, with but two exceptions, to what
the philosophy of contemporary physics has to say about the object of
scientific knowledge qua object, independent of its relation to the
scientist as knower.In short,
we have been concerned with its
ontology.This philosophy also
has its epistemological component.This component falls into three parts: (1) The relation between (a)
the directly observed data given to the physicist as inductive knower in his
observations or his experiments and (b) the speculatively proposed,
indirectly verified, axiomatically constructed postulates of his theory.The latter term (b)
defines the objects of scientific knowledge qua object and, hence,
gives the ontology.The
relation between (a) and (b) defines one factor in the epistemology.(2) The role of the concept of probability in the theory of
errors, by means of which the physicist defines the criterion for judging
how far his experimental findings can depart, due to errors of human
experimentation, from the deduced consequences of the postulates of the
theory and still be regarded as confirming the theory.(3) The effect of the experiment being performed upon the
object being known.What
Heisenberg says about the first and second of these three epistemological
factors in contemporary physics has already been emphasized in this
Introduction.It remains to
direct the reader’s attention to what he says about item (3).

In
modern physical theory, previous to quantum mechanics, (3) played no role
whatever.Hence, the
epistemology of modern physics was then completely specified by (1) and (2)
alone.In quantum mechanics, however, (3) (as well as (1) and
(2)) becomes very important.The
very act of observing alters the object being observed when its
quantum numbers are small.From this fact
Heisenberg draws a very important conclusion concerning the relation between the object, the observing physicist,
and the rest of the universe.This
conclusion can be appreciated if attention is directed to the following key
points.It may be recalled that in some of the definitions of
mechanical causality given earlier in this Introduction, the qualifying
words “for an isolated system”
were added; elsewhere it was implicit.This qualifying condition can be satisfied in principle in
Newtonian and Relativistic mechanics, and also in practice by making
more and more careful observations and refinements in one’s
experimental instruments.The
introduction of the concept of probability into the definition of state of
the object of scientific knowledge in quantum mechanics rules out, however,
in principle, and not merely in practice due to the imperfections of human
observation and instruments, the satisfying of the condition that the object
of the physicist’s knowledge is an isolated system.Heisenberg shows also that the including of the experimental
apparatus and even of the eye of the observing scientist in the
physical system which is the object of the knower’s knowledge does not
help, since, if quantum mechanics be correct, the states of all objects have
to be defined in principle by recourse to the
concept of probability.Consequently,
only if the whole universe is included in the object of scientific
knowledge can the qualifying condition “for an isolated system” be
satisfied for even the weaker form of
mechanical causation.Clearly,
the philosophy of contemporary physics is shown by this book to be as
novel in its epistemology as it is in its ontology.Indeed, it is from the originality of its ontology-the consistent
unification of potentiality and
mechanical causality in its weaker form-that the novelty of its epistemology arises.

Unquestionably,
one other thing is clear.An
analysis of the specific experimentally verified theories of modern physics with respect
to what they say about the object of human knowledge and its relation to the
human knower exhibits a very rich and complex ontological and
epistemological philosophy which is an
essential part of the scientific theory and method itself.Hence, physics is neither epistemologically nor ontologically
neutral.Deny anyone of the
epistemological assumptions of the physicist’s theory and there is no
scientific method for testing whether what the theory says about the
physical object is true, in the sense of being empirically confirmed.Deny anyone of the ontological assumptions and there is not enough content in the
axiomatically constructed mathematical postulates of the physicist’s
theory to permit the deduction of the experimental facts which it is
introduced to predict, co-ordinate consistently and explain.Hence, to the extent that experimental physicists assure US
that their theory of contemporary physics is indirectly and experimentally verified, they ipso facto assure us that its rich
and complex ontological and epistemological philosophy is verified also.

When
such empirically verified philosophy of the true in the natural sciences is
identified with the criterion of the good and the just in the humanities and
the social sciences, one has natural-law ethics and jurisprudence.In other words, one has a scientifically meaningful cognitive
criterion and method for judging both the verbal, personal and social norms
of the positive law and the living ethos embodied in the customs, habits and
traditional cultural institutions of the de facto peoples and cultures
of the world.It is the coming
together of this new philosophy of physics with the respective
philosophies of culture of mankind that is the major event in today’s and
tomorrows world.At this point,
the philosophy of physics in this book and its important reference to the
social consequences of physics come together.

The
chapters of this book have been read as Gifford Lectures at
the University of St.Andrews
during the winter term 1955-56.According to the will of their founder the Gifford Lectures should
“freely discuss all questions about man’s conceptions of God or the
Infinite, their origin, nature, and truth, whether he can have any such
conceptions, whether God is under any or what limitations and so on.” The
lectures of Heisenberg do not attempt
to reach these most general and most difficult problems.

But
they try to go far beyond the limited scope of a special science into the
wide field of those general human problems that have
been raised by the enormous recent development and the far-reaching
practical applications of natural science.

When
war breaks out people say its stupid and cannot last long.But being stupid does not prevent it from lasting.Stupidity has a knack of getting its way, which we would see if we
were not always so wrapped up in ourselves.

—Albert
Camus

What
is a rebel?A man who says
no—but whose refusal does not imply a renunciation.He is also a man who says yes as soon as he begins to think for
himself.He rebels because he
categorically refuses to submit to conditions that he considers intolerable and also because he is
confusedly convinced that his position is justified, or rather,
because in his own mind he thinks
that he has the right to.

—Albert
Camus

I
grew in the sea and poverty was my wealth, then I lost the sea, then all
luxury seemed grey, poverty intolerable.Since then, I wait.I
wait for the return voyage, the house by the sea, the clear light of day.I wait, I struggle to be polite.People see me pass in elegant cultured streets, I admire the views, I
applaud like everyone else, I shake hands, it’s not really me speaking.People praise me, I daydream a little, I’m offended, but show
almost no surprise.Then I
forget and smile at whoever insults me, or I greet those I love too
courteously.What’s to be
done if I can only remember a single image? Finally they urge me to say who I am.Still nothing, still nothing.

—Albert
Camus

In this vast cosmic
picture the abyss between macrocosmos and microcosmos—the very big and the
very little—will be bridged, and the whole complex of the universe will
resolve into a homogeneous fabric in which matter and energy are
indistinguishable and all forms of motion from the slow wheeling of the
galaxies to the wild flight of electrons become simply changes in the
structure and concentration of the primordial field.

When
one speaks today of modem
physics, the first thought is of atomic weapons.Everybody realizes the enormous influence of these weapons on the
political structure of our present world and is willing to admit that the
influence of physics on the general situation is greater than it ever has
been before.But is the
political aspect of modem physics really the most important one?When the world has adjusted itself in its political structure to the
new technical possibilities, what then will remain of the influence of modem physics?

To
answer these questions, one has to remember that every tool carries with it
the spirit by which it has been created.Since every nation and every political group has to be interested in
the new weapons in some way irrespective of the location and of the cultural
tradition of this group, the spirit of modem physics will penetrate into the
minds of many people and will connect itself in different ways with the
older traditions.What will be
the outcome of this impact of a special branch of modem science on different
powerful old traditions?In
those parts of the world in which modem science has been developed the
primary interest has been directed
for a long time toward practical activity, industry
and engineering combined with a rational analysis of the
outer and inner conditions for such activity.Such people will find it rather easy to cope with the new
ideas since they have had time for a
slow and gradual adjustment to the modern scientific methods of
thinking.In other parts of the world these ideas would be confronted
with the religious and philosophical foundations of the native culture.Since it is true that the results of
modern physics do touch such fundamental concepts as reality,
space and time, the confrontation may lead to entirely new
developments which cannot yet be foreseen.One characteristic feature of this meeting between modern science and
the older methods of thinking will be its complete internationality.In this exchange of thoughts the one side, the old tradition, will be
different in the different parts of the world, but the other side will be
the same everywhere and therefore the results of this exchange will be
spread over all areas in which the discussions take
place.

For
such reasons it may not be an unimportant task to try to discuss these ideas
of modern physics in a not too technical language, to study their
philosophical consequences, and to compare them with some of the older
traditions.The best way to
enter into the problems of modern physics may be by a historical description
of the development of quantum theory.It
is true that quantum theory is only a small sector of atomic physics and
atomic physics again is only a very small sector of modern science.Still it is in quantum theory that the most fundamental changes with
respect to the concept of reality have taken place, and in quantum theory in
its final form the new ideas of atomic physics are concentrated and
crystallized.The enormous and
extremely complicated experimental equipment needed for research in nuclear
physics shows another very impressive aspect of this part of modern science.But with regard to the
experimental technique nuclear physics represents the extreme
extension of a method of research which has determined the
growth of modern science ever since Huygens or Volta or Faraday.In a similar sense the discouraging mathematical complication of some
parts of quantum theory may be said to represent the extreme consequence of
the methods of Newton or Gauss or Maxwell.But the change in the concept of reality manifesting itself in
quantum theory is not simply a continuation of the past; it seems to be a
real break in the structure of modern science.Therefore, the first of the following chapters will be devoted
to the study of the historical development of quantum theory.

The
definition of risk is that more things can happen than will happen.

—Peter
Bernstein

Sweet and bitter, cold and warm as well as all the colors, all these
things exist but in opinion and not in reality—what really exists are
unchangeable particles, atoms, and their motions in empty space.

—Democritus

All
the choir of heaven and furniture of earth—in a word all those bodies
which compose the mighty frame of the world—have not any substance without
the mind.So long as they are
not perceived by me, or do not exist in my mind or in the mind of any
spirit, they have no existence whatsoever.

—Bishop
George Berkeley

May
I, monsieur, offer my services without running the risk of intruding?I fear you may not be able to make yourself understood by the worthy
ape who presides over the fate of this establishment.In fact, he speaks nothing but Dutch.Unless you authorize me to plead your case, he will not guess that
you want gin.There, I dare
hope he understood me—that nod must mean that he yields to my arguments.He is taking steps—indeed, he is making haste with prudent
deliberation.You are
lucky—he didn’t grunt.When
he refuses to serve someone he merely grunts.No one insists.Being
master of one’s moods is the privilege of the larger animals.Now I shall withdraw, monsieur, happy to have been of help to you.Thank you—I’d accept if I were sure of not being a nuisance.You are too kind.Then I
shall bring my glass over beside yours.

The
origin of quantum theory is connected with a well-known phenomenon, which did not belong to the central parts of atomic physics.Any piece of matter when it is heated starts to glow, gets red hot
and white hot at higher temperatures.The
color does not depend much on the surface of the material, and for a
black body it depends solely on the temperature.Therefore, the
radiation emitted by such a black body at high temperatures is a
suitable object for physical research; it is a simple phenomenon that should
find a simple explanation in terms of the
known laws for radiation and heat.The
attempt made at the end of the
nineteenth century by Lord Rayleigh and Jeans failed, however, and revealed serious difficulties.It would not be possible to describe these difficulties here in
simple terms.It must be
sufficient to state that the application of the known laws did not
lead to sensible results.When
Planck entered this line of
research in 1895 he tried to turn the problem from radiation to the radiating atom.This turning did not remove any of the difficulties inherent in the
problem, but it simplified the interpretation of the empirical facts.It was just at this time, during
the summer of 1900, that Curlbaum and Rubens in Berlin had made very
accurate new measurements of the spectrum of soheat radiation.When
Planck heard of these results he tried to represent
them by simple mathematical formulas which looked plausible from his
research on the general connection between heat
and radiation.One day Planck
and Rubens met for tea in
Planck’s home and compared Rubens’ latest results with a new formula
suggested by Planck.The comparison showed a complete agreement.This was the discovery of Planck’s law of heat
radiation.

It
was at the same time the beginning of intense theoretical work for Planck.What was the correct physical interpretation of
the new formula?Since Planck
could, from his earlier work, translate
his formula easily into a statement about the radiating atom (the so-called
oscillator), he must soon have found that his formula looked as if the
oscillator could only contain discrete quanta of energy—a result that was
so different from anything known in classical physics that he certainly must
have refused to believe it
in the beginning.But in a
period of most intensive work
during the summer of 1900 he finally convinced himself that there was no way
of escaping from this conclusion.It
was told by Planck’s son
that his father spoke to him about his new ideas on a long walk through the
Grunewald, the wood in the suburbs of Berlin.On this walk he explained that he felt he had possibly made a
discovery of the first rank, comparable perhaps only
to the discoveries of Newton.So
Planck must have realized at this time that his formula had touched the
foundations of our description of nature, and that these foundations would
one day start to move from their traditional present location toward a new
and as yet unknown position of stability.Planck, who was conservative in his whole outlook, did not
like this consequence at all, but he published his quantum hypothesis in
December of 1900.

The
idea that energy could be emitted or absorbed only in discrete energy quanta was so new that it could not be fitted into the
traditional framework of physics.An
attempt by Planck to reconcile
his new hypothesis with the older laws of radiation failed
in the essential points.It
took five years until the next step could
be made in the new direction.

This
time it was the young Albert Einstein, a revolutionary genius among
the physicists, who was not afraid to go further away
from the old concepts.There
were two problems in which he
could make use of the new ideas.One
was the so-called photoelectric effect, the emission of electrons from
metals under the influence of
light.The experiments,
especially those of Lenard,
had shown that the energy of the emitted electrons did not
depend on the intensity of the light, but only on its color or, more
precisely, on its frequency.This
could not be understood on the basis of the traditional theory of radiation.Einstein could explain the observations by interpreting
Planck’s hypothesis as saying that light consists of quanta of energy
traveling through space.The
energy of one light quantum should, in agreement with Planck’s
assumptions, be equal to the frequency of the light multiplied by Planck’s
constant.

The
other problem was the specific heat of solid bodies.The traditional theory led to values for the specific heat
which fitted the observations at higher temperatures but disagreed with them
at low ones.Again Einstein was able to show that one could understand
this behavior by applying the quantum hypothesis to the elastic
vibrations of the atoms in the solid body.These two results marked a
very important advance, since they revealed
the presence of Planck’s quantum of action-as his constant is called among
the physicists-in several phenomena, which had nothing immediately to do
with heat radiation.They revealed at the same time the deeply revolutionary character of the
new hypothesis, since the first of them led to a description of light
completely different from the traditional wave picture.Light could either be interpreted as consisting of electromagnetic
waves, according to Maxwell’s theory, or as consisting of light quanta,
energy packets traveling through space with high velocity.But could it be both?Einstein
knew, of course, that the well-known phenomena of diffraction and
interference could be explained
only on the basis of the wave picture.He was not able to dispute the complete contradiction between this
wave picture and the idea of the light quanta; nor did he even
attempt to remove the inconsistency
of this interpretation.He
simply took the contradiction
as something which would probably be understood
only much later.

In
the meantime the experiments of Becquerel, Curie and Rutherford had
led to some clarification concerning the structure
of the atom.In 1911
Rutherford’s observations on the interaction of a-rays penetrating
through matter resulted in his famous
atomic model.The atom is
pictured as consisting of a nucleus, which is positively charged and
contains nearly the total mass of
the atom, and electrons, which circle around the nucleus like the planets
circle around the sun.The
chemical bond between atoms of
different elements is explained as an interaction between the outer
electrons of the neighboring atoms; it has not directly
to do with the atomic nucleus.The
nucleus determines the chemical behavior of the atom through its charge
which in turn fixes the number
of electrons in the neutral atom.Initially
this model of the atom could not explain the most characteristic feature
of the atom, its enormous stability.No
planetary system following the laws of Newton’s mechanics would ever go
back to its original configuration after a collision with another
such system.But an atom of the element carbon, for instance, will still remain a
carbon atom after any collision or interaction in chemical
binding.

The
explanation for this unusual stability was given by Bohr in 1913,
through the application of Planck’s quantum hypothesis.If the atom can change its energy only by discrete energy
quanta, this must mean that the atom can exist only in discrete
stationary states, the lowest of which is the normal state of the atom.Therefore, after any kind of interaction the atom will finally always
fall back into its normal state.

By
this application of quantum theory to the atomic model, Bohr could
not only explain the stability of the atom but also, in some simple cases,
give a theoretical interpretation of the line spectra emitted by the atoms
after the excitation through electric discharge
or heat.His theory rested upon
a combination of classical
mechanics for the motion of the electrons with quantum conditions,
which were imposed upon the classical motions for defining the discrete
stationary states of the system.A
consistent mathematical
formulation for those conditions was later given by Sommerfeld.Bohr was
well aware of the fact that the quantum conditions spoil in some way the
consistency of Newtonian mechanics.In the simple case of the hydrogen atom one could calculate from
Bohr’s theory the frequencies of the light emitted by
the atom, and the agreement with the observations was perfect.Yet these frequencies were different from the orbital frequencies
and their harmonics of the electrons circling around the nucleus, and this
fact showed at once that the theory was still full
of contradictions.But it
contained an essential part of the truth.It did explain qualitatively the chemical behavior of the atoms and
their line spectra; the existence of the discrete stationary
states was verified by the experiments of Franck and Hertz, Stern and
Gerlach.

Bohr’s
theory had opened up a new line of research.The great amount of
experimental material collected by spectroscopy through several decades was
now available for information about
the strange quantum laws governing the motions of the electrons
in the atom.The many
experiments of chemistry could be
used for the same purpose.It
was from this time on that the physicists learned to ask the right
questions; and asking the right question is frequently more than halfway to
the solution of the problem.

What
were these questions?Practically
all of them had to do with the strange apparent contradictions between the
results of different experiments.How could it be that the same radiation that produces
interference patterns, and therefore must consist of waves, also produces
the photoelectric effect, and therefore must
consist of moving particles?How
could it be that the frequency of the orbital motion of the electron in the
atom does not show up in the
frequency of the emitted radiation?Does
this mean that there is no orbital motion?But if the idea of orbital motion
should in incorrect, what happens to the electrons inside
the atom?One can see the electrons move through a cloud chamber, and
sometimes they are knocked out of an atom; why should they not also
move within the atom?It is
true that they might be at rest in the normal state of the atom, the state
of lowest energy.But there are many states of higher energy, where the
electronic shell has an angular momentum.There the electrons
cannot possibly be at rest.One
could add a number of similar examples.Again and again one found that the attempt to describe atomic events
in the traditional terms of physics led to contradictions.

Gradually,
during the early twenties, the physicists became accustomed to these
difficulties, they acquired a certain vague knowledge about where trouble
would occur, and they learned to avoid contradictions.They knew which description of an atomic event would be the correct
one for the special experiment under
discussion.This was not sufficient to form a consistent general
picture of what happens in a quantum process, but it changed
the minds of the physicists in such a way that they somehow got into the spirit of quantum theory.Therefore, even some
time before one had a consistent formulation of quantum theory
one knew more or less what would be the result of any experiment.

One
frequently discussed what one called ideal experiments.Such experiments were
designed to answer a very critical question irrespective of whether or not they could actually be carried-out.Of course it was important that it should be possible in principle
to carry out the experiment, but the technique might be extremely
complicated.These ideal
experiments could be very useful in clarifying certain problems.If there was no agreement among the physicists about
the result of such an ideal experiment,
it was frequently possible to find a similar but simpler experiment
that could be carried out, so that the experimental answer contributed
essentially to the clarification of quantum theory.

The
strangest experience of those years was that the paradoxes of quantum theory did not disappear during this process of clarification;
on the contrary, they became even more marked and
more exciting.There was, for
instance, the experiment of Compton on the scattering of X-rays.From earlier experiments on the interference of scattered light there could be no doubt that
scattering takes place essentially in the following way: The incident
light wave makes an electron in the beam vibrate in the frequency of the
wave; the oscillating electron then emits a spherical wave with the same frequency and thereby produces the
scattered light.However, Compton found in 1923 that the frequency of
scattered X-rays was different from the frequency of the incident
X-ray.This change of frequency
could be formally understood by assuming that scattering is to be described
as collision of a light quantum with an electron.The energy of the light quantum is changed during the collision; and
since the frequency times Planck’s constant should be the energy of the
light quantum, the frequency also should be changed.But what happens in this
interpretation of the light wave?The
two experiments-one on the interference of scattered light and the
other on the change of frequency of the scattered light-seemed to contradict
each other without any possibility of compromise.

By
this time many physicists were convinced that these apparent
contradictions belonged to the intrinsic structure of atomic physics.Therefore, in 1924 de Broglie in France tried to extend the dualism
between wave description and particle description to the elementary
particles of matter, primarily to the electrons.He showed that a certain matter wave could “correspond” to
a moving electron, just as a light wave corresponds to a moving light
quantum.It was not clear at
the time what the word
“correspond” meant in this connection.But de Broglie suggested
that the quantum condition in Bohr’s theory should be interpreted as a statement about the matter waves.A wave circling around a nucleus can for geometrical reasons
only be a stationary wave; and the perimeter of the orbit must be an integer
multiple of the wave length. In
this way de Broglie’s idea connected the quantum condition, which always
had been a foreign element in the mechanics of the electrons, with the dualism between
waves and particles.

In
Bohr’s theory the discrepancy between the calculated orbital frequency of
the electrons and the frequency of the emitted radiation had to be
interpreted as a limitation to the concept of the electronic orbit.This concept had been somewhat doubtful from the beginning.For the higher orbits, however, the electrons should move at a large
distance from the nucleus just as
they do when one sees them moving through a cloud chamber.There one should speak about electronic orbits.It was therefore very
satisfactory that for these higher orbits the frequencies of the emitted
radiation approach the orbital frequency and
its higher harmonics.Also Bohr
had already suggested in his early papers that the intensities of the
emitted spectral lines approach the intensities of the corresponding
harmonics.This principle of
correspondence had proved very useful for the approximative calculation of
the intensities of spectral lines.In
this way one had the impression that Bohr’s theory gave a qualitative but
not a quantitative description of what happens inside the atom;
that some new feature of the behavior of matter was qualitatively
expressed by the quantum conditions, which in turn
were connected with the dualism between waves and particles.

The
precise mathematical formulation of quantum theory finally emerged from two
different developments.The one
started from Bohr’s principle of correspondence.One had to give up the
concept of the electronic orbit but still had to maintain it in the limit of
high quantum numbers, i.e., for the large orbits.In this latter case the emitted radiation, by means of its
frequencies and intensities, gives a picture of the electronic orbit; it
represents what the mathematicians call a Fourier expansion of
the orbit.The idea suggested
itself that one should write down the
mechanical laws not as equations for the positions and velocities of
the electrons but as equations for the frequencies and amplitudes of their
Fourier expansion.Starting
from such equations and changing them very little one could hope to come to relations for those quantities which correspond to the frequencies
and intensities of the emitted radiation, even for the small
orbits and the ground state of the atom.This plan could actually be carried out; in the summer of 1925
it led to a mathematical formalism called matrix mechanics or, more generally,
quantum mechanics.The
equations of motion in Newtonian
mechanics were replaced by similar equations between matrices; it was a
strange experience to find that many of the
old results of Newtonian mechanics, like conservation of energy, etc, could
be derived also in the new scheme.Later
the investigations of Born,
Jordan and Dirac showed that the matrices
representing position and momentum of the electron do not commute.This latter fact demonstrated clearly the essential difference
between quantum mechanics and classical mechanics.

The
other development followed de Broglie’s idea of matter waves.Schrödinger tried to set up a wave equation for de Broglie’s
stationary waves around the nucleus.Early
in 1926 he succeeded in deriving the energy values of the stationary states
of the hydrogen atom as “Eigenvalues” of his wave equation and could
give a more general prescription for transforming a given set of classical
equations of motion into a corresponding Wave
equation in a space of many dimensions.Later he was able to
prove that his formalism of wave mechanics was mathematically equivalent to
the earlier formalism of quantum mechanics.Thus one finally had a consistent mathematical formalism, which could be defined in two equivalent ways starting either from
relations between matrices or from wave equations.This formalism gave
the correct energy values for the hydrogen atom; it took less than one year
to show that it was also successful for the
helium atom and the more complicated problems of the heavier atoms.But in what
sense did the new formalism describe the atom?The paradoxes of the dualism between wave picture and particle
picture were not solved; they were hidden somehow in the mathematical scheme.

A
first and very interesting step toward a real understanding of quantum
theory was taken by Bohr, Kramers and Slater in 1924.These authors tried to solve the apparent contradiction between the
wave picture and the particle picture by the concept of the probability wave.The
electromagnetic waves were interpreted not as “real” waves but as
probability waves, the intensity of which determines in every point the
probability for the absorption (or induced emission) of a light quantum by
an atom at this point.This idea led to the conclusion that the laws of conservation
of energy and momentum need not be true for the single event, that they are
only statistical laws and are true only
in the statistical average.This
conclusion was not correct, however, and the connections between the wave
aspect and the particle aspect of radiation were still more complicated.

But
the paper of Bohr, Kramers and Slater revealed one essential feature of the
correct interpretation of quantum theory.This concept of the
probability wave was something entirely new in theoretical physics
since Newton.Probability in
mathematics or in statistical mechanics means a statement about our degree of
knowledge of the actual situation.In
throwing dice we do not know
the fine details of the motion of our hands which determine
the fall of the dice and therefore we say that the probability
for throwing a special number is just one in six.The probability wave of
Bohr, Kramers, Slater, however, meant more
than that; it meant a tendency for something.It was a quantitative version of the old concept of
“potentia” in Aristotelian philosophy.It introduced something standing in the middle
between the idea of an event and the actual event, a strange kind of
physical reality just in the middle between possibility and reality.

Later
when the mathematical framework of quantum theory was fixed, Born took up this idea of the probability wave and gave
a clear definition of the mathematical quantity in the formalism,
which was to be interpreted as the probability wave.It was not a three-dimensional wave like elastic or radio
waves, but a wave in the many-dimensional configuration space, and
therefore a rather abstract mathematical quantity.

Even
at this time, in the summer of 1926, it was not clear in every case how the mathematical formalism should be used to describe
a given experimental situation.One
knew how to describe the
stationary states of an atom, but one did not know how to describe a much
simpler event-as for instance an electron moving through a cloud chamber.

When
Schrödinger in that summer had shown that his formalism of wave mechanics
was mathematically equivalent to quantum mechanics he tried for some time to
abandon the idea of quanta and
“quantum jumps” altogether and to replace the electrons in the atoms
simply by his three-dimensional matter waves.He was inspired to this attempt by his result, that the energy
levels of the hydrogen atom in his theory seemed to be simply
the eigenfrequencies of the stationary matter waves.Therefore, he
thought it was a mistake to call them energies; they were just frequencies.But
in the discussions which took place
in the autumn of 1926 in Copenhagen between Bohr and Schrödinger and
the Copenhagen group of physicists it soon became
apparent that such an interpretation would not even be sufficient to
explain Planck’s formula of heat radiation.

During
the months following these discussions an intensive study of all questions
concerning the interpretation of quantum theory in Copenhagen finally led to
a complete and, as many physicists believe, satisfactory clarification of
the situation.But it was
not a solution which one could easily accept.I remember discussions with Bohr which went through many hours
till very late at night and ended almost in despair; and when at the end of
the discussion I went alone for a walk in the neighboring park I
repeated to myself again and again the question: Can nature possibly
be as absurd as it seemed to us in these atomic experiments?

The
final solution was approached in two different ways.The one was a turning
around of the question.Instead
of asking: How can one in
the known mathematical scheme express a given experimental situation?the other question was put: Is it true, perhaps, that only
such experimental situations can arise in nature as can be expressed in the
mathematical formalism?The
assumption that this was actually true led to limitations in the use of
those concepts that had been the basis of classical physics since Newton.One could speak of the position and of the velocity of an electron as
in Newtonian mechanics and one could observe and measure these quantities.But one could not fix both quantities simultaneously with an
arbitrarily high accuracy.Actually the product of these two inaccuracies turned out to
be not less than Planck’s constant divided by the mass of the particle.Similar relations could be formulated for other experimental
situations.They are usually
called relations of uncertainty
or principle of indeterminacy.One
had learned that the old
concepts fit nature only inaccurately.

The
other way of approach was Bohr’s concept of complementary.Schrödinger had described
the atom as a system not of a
nucleus and electrons but of a nucleus and matter waves.This picture of the matter waves certainly also contained an element
of truth.Bohr considered the
two pictures-particle picture and wave picture-as two complementary
descriptions of the same
reality.Any of these
descriptions can be only partially true,
there must be limitations to the use of the particle concept as well as of
the wave concept, else one could not avoid contradictions.If one takes into account those limitations which can be expressed
by the uncertainty relations, the contradictions disappear.

In
this way since the spring of 1927 one has had a consistent interpretation of quantum theory, which is frequently called the “Copenhagen
interpretation.” This interpretation received its crucial test in
the autumn of 1927 at the Solvay conference in Brussels.Those experiments which had always led to the worst paradoxes
were again and again discussed in all details, especially by Einstein.New
ideal experiments were invented to trace any possible inconsistency
of the theory, but the theory was shown to be consistent and seemed to fit
the experiments as far as one could see.

The
details of this Copenhagen interpretation will be the subject of the
next chapter.It should be
emphasized at this point that it has taken more than a quarter of a century
to get from the first idea of the existence of energy quanta to a real
understanding of the quantum theoretical laws.This indicates the great change that had to take place in the
fundamental concepts concerning reality before one could understand the new
situation.

The
hard sphere has always a definite position in space; the electron apparently has
not. A hard sphere takes up a very definite amount of room; an electron—well
it is probably as meaningless to discuss how much room an electron takes up
as it is to discuss how much room a fear, an anxiety, or an uncertainty
takes up.

—Sir James
Jeans

The
fundamental question of whether light is waves or particles has never been
answered. The dual character of light is, however, only one aspect of a
deeper and more remarkable duality which pervades all nature.

—Lincoln
Barnett

Those
who believe in God strictly of the basis of faith are setting themselves up
for failure for the reason that their conception of God is based on a static
snapshot that is, by definition, not subject to reason.The Devil is the one who seeks out those who blindly follow.A true God most certainly wants to be constantly challenged by both
faith and reason.Kevin Spacey
tells us in the 1996 movie The Usual Suspects that the greatest trick the
Devil ever pulled was convincing the world he doesn’t exist.And now we know the second greatest trick the Devil ever pulled was
convincing the world we can know God by faith alone.

—Christopher
Bek

Of
whom and of what indeed can I say—I know that!This heart within me I can feel, and I judge that it exists.This world I can touch, and I likewise judge that it exists.There ends all my knowledge, and the rest is construction.For if I try to seize this self of which I feel sure, if I try to
define and summarize it, it is nothing but water slipping through my
fingers.I can sketch one by
one all the aspects that it is able to assume, all those likewise that have
been attributed to it, this upbringing, this origin, this ardor of these
silences, this nobility or this vileness.But aspects cannot be added up.This very heart which is mine will forever remain undefinable to me.Between the certainty I have of my existence and the content I try to
give to that assurance, the gap will never be filled.Forever I shall be a stranger to myself.In psychology as in logic, there are truths but no truth.Socrates’ Know thyself has as much value as the Be virtuous of our
confessionals.They reveal a
nostalgia at the same time as an ignorance.They are sterile exercises on great subjects.They are legitimate insofar as they are approximate.

The
Copenhagen interpretation of quantum theory starts from a paradox.Any experiment in
physics, whether it refers to the phenomena
of daily life or to atomic events, is to be described in
the terms of classical physics.The
concepts of classical physics
form the language by which we describe the arrangement of our experiments
and state the results.We
cannot and should not replace these concepts by any others.Still the application of these concepts is limited by the relations
of uncertainty.We must keep in mind this limited range of applicability of the
classical concepts while using them, but we cannot and
should not try to improve them.

For
a better understanding of this paradox it is useful to compare the
procedure for the theoretical interpretation of an experiment
in classical physics and in quantum theory.In Newton’s mechanics, for instance, we may start by measuring the position
and the velocity of the planet whose motion we are going to study.The result of the observation is translated into mathematics by
deriving numbers for the coordinates and the momenta of the planet from the
observation.Then the equations
of motion are used to derive from these values of the coordinates and
momenta at a given time the values of these coordinates or any other
properties of the system at a later time, and in this way the astronomer can
predict the properties of the system at a later
time.He can, for instance,
predict the exact time for an eclipse
of the moon.

In
quantum theory the procedure is slightly different.We could for instance be interested in the motion of an
electron through a cloud chamber
and could determine by some kind of observation
the initial position and velocity of the electron.But this
determination will not be accurate; it will at least contain the inaccuracies following from the uncertainty relations and will
probably contain still larger errors due to the difficulty of the
experiment.It is the first of
these inaccuracies which allows us to translate the result of the
observation into the mathematical scheme of quantum theory.A probability function is written down which represents the
experimental situation at the time of the measurement, including even the
possible errors of the
measurement.

This
probability function represents a mixture of two things, partly a
fact and partly our knowledge of a fact.It represents a fact in so
far as it assigns at the initial time the probability unity (ie.
complete certainty) to the initial situation: the electron moving with the
observed velocity at the observed position; “observed” means observed
within the accuracy of the experiment.It represents our knowledge in so far as another observer could
perhaps know the position of the electron more accurately.The error in the experiment
does—at least to some
extent-not represent a property of the electron but a deficiency in
our knowledge of the electron.Also
this deficiency of knowledge is expressed in the probability function.

In
classical physics one should in a careful investigation also consider the error of the observation.As a result one would get a probability distribution
for the initial values of the coordinates and velocities and therefore
something very similar to the probability
function in quantum mechanics.Only
the necessary uncertainty due
to the uncertainty relations is lacking in classical physics.

When
the probability function in quantum theory has been determined at the initial time from the observation, one can from
the laws of quantum theory calculate the probability function at any
later time and can thereby determine the probability for a measurement
giving a specified value of the measured quantity.We can, for instance, predict the probability for finding the
electron at a later time at a given point in the cloud chamber.It should be emphasized, however, that the probability function does
not in itself represent a course of events in the course of time.It represents a tendency for events and our knowledge
of events.The probability
function can be connected with
reality only if one essential condition is fulfilled: if a new measurement is made to determine a certain property of the system.Only then does the probability function allow us to calculate
the probable result of the new measurement.The result of the measurement again will be stated in terms of
classical physics.

Therefore,
the theoretical interpretation of an experiment requires three
distinct steps: (1) the translation of the initial experimental situation
into a probability function; (2) the following up of this function in the
course of time; (3) the statement of
a new measurement to be made of the system, the result of which can then be
calculated from the probability function.For the first step the fulfillment of the uncertainty relations is a
necessary condition.The second
step cannot be described in terms of the classical concepts; there is no
description of what happens to the system between the initial observation
and the next measurement.It is only in the third step that we change over again
from the “possible” to the “actual.”

Let
us illustrate these three steps in a simple ideal experiment.It has been said that the atom consists of a nucleus and electrons
moving around the nucleus; it has also been stated that the concept of an
electronic orbit is doubtful.One
could argue that it should at least in principle be possible to observe the
electron in its orbit.One
should simply look at the atom through a microscope of a very high resolving
power, then one would see the electron moving in its orbit.Such a high resolving power could to be sure not be obtained by a
microscope using ordinary light, since the inaccuracy of the measurement of
the position can never be smaller
than the wavelength of the light.But
a microscope using
alpha-rays with a wavelength smaller than the size of the atom would
do.Such a microscope has not
yet been constructed but that should not prevent us from discussing the ideal
experiment.

Is
the first step, the translation of the result of the observation into a
probability function, possible?It
is possible only if the uncertainty relation is fulfilled after the
observation.The position of the electron will be known with an accuracy given by the wavelength
of the alpha-ray.The electron
may have been practically at rest before the observation.But in the act of observation at least one light quantum of
the alpha-ray must have passed the microscope and must first have been
deflected by the electron.Therefore,
the electron has been pushed by the light quantum, it has changed its
momentum and its velocity, and one can show that the
uncertainty of this change is just big enough to guarantee the validity of
the uncertainty relations.Therefore,
there is no difficulty with the first step.

At
the same time one can easily see that there is no way of observing the orbit of the electron around the nucleus.The second step shows a wave pocket moving not around the nucleus but
away from the atom, because the first light quantum will have knocked the
electron out from the atom.The
momentum of light quantum of
the alpha-ray is much bigger than the original momentum of the electron if
the wavelength of the alpha-ray is much smaller than the size of the atom.Therefore, the first light quantum is sufficient to knock the
electron out of the atom and one
can never observe more than one point in the orbit of the electron;
therefore, there is no orbit in the ordinary sense.The next
observation-the third step-will show the electron on its path from the atom.Quite
generally there is no way of describing what happens between two consecutive
observations.It is of
course tempting to say that the electron must have been somewhere
between the two observations and that therefore the electron
must have described some kind of path or orbit even if it may be impossible
to know which path.This would
be a reasonable argument in classical physics.But in quantum theory it
would be a misuse of the language which, as we will see later, cannot be justified.We can
leave it open for the moment, whether
this warning is a statement about the way in which we should
talk about atomic events or a statement about the events themselves, whether
it refers to epistemology or to ontology.In any case we have
to be very cautious about the wording of any
statement concerning the behavior of atomic particles.

Actually
we need not speak of particles at all.For many experiments it
is more convenient to speak of matter waves; for instance, of stationary
matter waves around the atomic nucleus.Such a description would directly contradict the other
description if one does not pay attention to the limitations given by the
uncertainty relations.Through
the limitations the contradiction is avoided.The use of “matter waves” is convenient, for example,
when dealing with the radiation emitted by the atom.By means of its frequencies and intensities the
radiation gives information about the oscillating charge distribution in the
atom, and there the wave picture
comes much nearer to the truth than the particle picture.Therefore, Bohr advocated the use of both pictures, which he called
“complementary” to each other.The
two pictures are of course mutually exclusive because a certain thing
cannot at the same time be a
particle (ie. substance confined to a very small volume) and a wave (ie. a
field spread out over a large space), but the two complement each other.By playing with both pictures, by going from the one picture to the other and
back again, we finally get the right impression of the strange kind
of reality behind our atomic experiments.Bohr uses the concept of “complementary” at several places
in the interpretation of quantum theory.The knowledge of the position of a particle is complementary to the
knowledge of its velocity or momentum.If we know the one with high accuracy we cannot know the other with
high accuracy; still we must know both for determining
the behavior of the system.The
space-time description of the
atomic events is complementary to their deterministic description.The probability function obeys an equation of motion
as the coordinates did in Newtonian mechanics; its change in the course of
time is completely determined by the quantum mechanical equation, but it
does not allow a descrip­tion in space and time.The observation, on the other hand, enforces the description in space
and time but breaks the determined
continuity of the probability function by changing our knowledge
of the system.

Generally
the dualism between two different descriptions of the same reality is no
longer a difficulty since we know from the
mathematical formulation of the theory that contradictions cannot
arise.The dualism between the
two complementary pictures-waves
and particles-is also clearly brought out in the flexibility of the
mathematical scheme.The
formalism is normally written
to resemble Newtonian mechanics, with equations
of motion for the coordinates
and the momenta of the particles.But
by a simple transformation it can be rewritten to resemble a wave equation
for an ordinary three-dimensional matter wave.Therefore, this
possibility of playing with
different complementary
pictures has its analogy in the different transformations of
the mathematical scheme; it does not lead to any difficulties in
the Copenhagen interpretation of quantum theory.

A
real difficulty in the understanding of this interpretation arises, however,
when one asks the famous question: But what happens “really” in
an atomic event?It has been
said before that the mechanism and the results of an observation can always
be stated in terms of the classical concepts.But what one deduces from an
observation is a probability function, a mathematical
expression that combines statements about possibilities or tendencies
with statements about our knowledge of facts.So we cannot completely
objectify the result of an observation,
we cannot describe what
“happens” between this observation and the next.This looks as if we
had introduced an element of subjectivism into the theory, as if we meant to
say: what happens depends on our
way of observing it or on the fact that
we observe it.Before discussing
this problem of subjectivism
it is necessary to explain quite clearly why one would get into hopeless difficulties if one tried
to describe what happens between two consecutive observations.

For
this purpose it is convenient to discuss the following ideal experiment:
We assume that a small source of monochromatic light radiates toward a black
screen with two small holes in it.The
diameter of the holes may be not much bigger than the wavelength
of the light, but their distance will be very much bigger.At some distance behind the screen a photographic
plate registers the incident light.If one describes this experiment in terms of the wave
picture, one says that the
primary wave penetrates
through the two holes; there will be secondary spherical waves
starting from the holes that interfere with one another, and
the interference will produce a pattern of varying intensity on
the photographic plate.

The
blackening of the photographic plate is
a quantum process, a chemical reaction produced by single light
quanta.Therefore, it must also be possible to describe the
experiment in terms of light quanta.If it would be permissible to say what happens
to the single light quantum between its emission from the
light source and its absorption in the photographic plate, one could
argue as follows: The single light quantum can come through
the first hole or through the second one.If it goes through the first hole and is scattered there, its
probability for being absorbed at a certain point of the photographic plate
cannot depend upon whether
the second hole is closed or open.The
probability distribution on the plate will be the same as if only the first
hole was open.If the
experiment is repeated many times and
one takes together all cases in which the light quantum has gone through the first hole, the blackening of the plate due to these
cases will correspond to this probability distribution.If one considers only those light quanta that go through the second
hole, the blackening should correspond to a probability distribution
derived from the assumption that only the second hole is open.The total blackening, therefore, should just be the sum of the
blackenings in the two cases; in other words, there should be I no interference pattern.But
we know this is not correct, and I the
experiment will show the interference pattern.Therefore, thestatement
that any light quantum must have gone either through I the
first orthrough the second hole is problematic and leads to contradictions.This example shows clearly that the concept of the probability
function does not allow a description of what happens
between two observations.Any
attempt to find such a description would lead to contradictions; this must
mean that the term “happens” is restricted to the observation.

Now,
this is a very strange result, since it seems to indicate that the
observation plays a decisive role in the event and that the
reality varies, depending upon whether we observe it or not.To make this point clearer we have to analyze the process of I observation
more closely.To
begin with, it is important to remember that in natural science
we are not interested in the universe as a whole, including ourselves, but
we direct our attention to some part of the universe
and make that the object of our studies.In atomic physics
this part is usually a very small object, an atomic particle or
a group of such particles, sometimes much larger-the size does not
matter; but it is important that a large part of the I
universe, including ourselves, does not belong to the object.

Now,
the theoretical interpretation of an experiment starts with the two steps
that have been discussed.In
the first step we have to
describe the arrangement of the experiment, eventually combined with a first
observation, in terms of classical physics and translate this description
into a probability function.This
probability function follows the laws of quantum theory, and its change
in the course of time, which is continuous, can be calculated from the initial conditions; this is the second step.The probability function combines objective and subjective elements.It contains statements about possibilities or better
tendencies (“potentia” in Aristotelian philosophy), and these statements
are completely objective, they do not depend on any observer; and it
contains statements about our knowledge of the system, which of course are
subjective in so far as they may be different for different observers.In ideal cases the subjective element in the
probability function may be practically negligible as compared with
the objective one.The physicists then speak of a “pure case.”

When
we now come to the next observation, the result of which should be predicted from the theory, it is very important to
realize that our object has to be in contact with the other part of the
world, namely, the experimental arrangement, the measuring rod, etc., before or at least at the moment of observation.This means that the
equation of motion for the probability function does now contain the
influence of the interaction with the measuring device.This influence introduces a new element of uncertainty, since
the measuring device is necessarily described in the terms of classical
physics; such a description contains all the uncertainties concerning the
microscopic structure of the device
which we know from thermodynamics, and since the device is connected
with the rest of the world, it contains in fact the uncertainties of the
microscopic structure of the whole world.These uncertainties may be called objective in so far as they are
simply a consequence of the description in the terms of classical physics
and do not depend on any observer.They
may be called subjective in so far as they refer to our incomplete knowledge
of the world.

After
this interaction has taken place, the probability function contains the
objective element of tendency and the subjective element of incomplete
knowledge, even if it has been a “pure case” before.It is for this reason that the result of the observation cannot
generally be predicted with certainty; what can be predicted is the
probability of a certain result of the observation, and this statement about
the probability can be checked by repeating
the experiment many times.The
probability function does,
unlike the common procedure in Newtonian mechanics, not describe a certain event but, at least during the process of
observation, a whole ensemble of possible events.The
observation itself changes the probability function discontinuously;
it selects of all possible events the actual one that has taken place.Since through the observation our knowledge of the system has changed
discontinuously, its mathematical representation
also has undergone the discontinuous change and we
speak of a “quantum jump.” When the old adage “Natura non
facit saltus” is used as
a basis for criticism of quantum theory,
we can reply that certainly our knowledge can change suddenly
and that this fact justifies the use of the term “quantum jump.”

Therefore,
the transition from the “possible” to the “actual” takes place during the act of observation.If we want to describe what happens in an atomic event, we
have to realize that the word “happens” can apply only to the
observation, not to the state
of affairs between two observations.It
applies to the physical, not
the psychical act of observation, and we may say that
the transition from the “possible” to the “actual” takes place
as soon as the interaction of the object with the measuring device,
and thereby with the rest of the world, has come into play; it is not
connected with the act of registration of the result by the mind of the observer.The
discontinuous change in the probability function, however, takes
place with the act of registration, because it is the discontinuous change
of our knowledge in the instant of registration that has its image in the
discontinuous change of the
probability function.

To
what extent, then, have we finally come to an objective description
of the world, especially of the atomic world?In classical physics science started from the belief-or should one say
from the illusion?-that we could describe the world or at least
parts of the world without any reference to ourselves.This is actually possible to a large extent.We know that the city of London exists whether we see it or
not.It may be said that classical
physics is just that idealization in which we can speak about parts
of the world without any reference to ourselves.Its success has led to the general ideal of an objective description
of the world.Objectivity has
become the first criterion for the value
of any scientific result.Does
the Copenhagen interpretation of quantum theory still comply with this
ideal?One may perhaps
say that quantum theory corresponds to this ideal as far as possible.Certainly quantum theory does not contain genuine subjective
features, it does not introduce the mind of the physicist
as a part of the atomic event.But
it starts from the division of the world into the “object” and
the rest of the world, and from the
fact that at least for the rest of the world we use the classical
concepts in our description.This
division is arbitrary and historically a direct consequence of our
scientific method; the use of the classical concepts is finally a
consequence of the general human
way of thinking.But this is
already a reference to
ourselves and in so far our description is not completely objective.

It
has been stated in the beginning that the Copenhagen interpretation of
quantum theory starts with a paradox.It
starts from the fact that we
describe our experiments in the terms of classical physics and at the same
time from the knowledge that these concepts do not fit nature accurately.The tension between these two starting points is the root of
the statistical character of quantum
theory.Therefore, it has
sometimes been suggested that
one should depart from the classical concepts altogether and that
a radical change in the concepts used for describing the experiments
might possibly lead back to a nonstatical, completely objective description of nature.This
suggestion, however, rests upon a misunderstanding.The concepts of
classical physics are just a refinement of the concepts of daily life and are an essential part of the language which forms the
basis of all natural science.Our
actual situation in science is
such that we do use the classical concepts for the description
of the experiments, and it was the problem of quantum theory to find
theoretical interpretation of the experiments on this basis.There is no use in discussing what could be done if we were other beings than we are.At
this point we have to realize, as von Weizsacker has put it, that
“Nature is earlier than man, but
man is earlier than natural science.” The first part of the
sentence justifies classical physics, with its ideal of complete objectivity.The second part tells us why we cannot escape the paradox of
quantum theory, namely, the necessity of using the classical concepts.

We
have to add some comments on the actual procedure in the quantum-theoretical interpretation of atomic events.It has been said that we always start with a division of the world into an
object, which we are going to study, and the rest of the world, and
that this division is to some extent arbitrary.It should indeed not
make any difference in the final result if we, for example, add some part of
the measuring device or the whole device to the object
and apply the laws of quantum theory to this more complicated object.It can be
shown that such an alteration of the theoretical treatment would not alter
the predictions concerning a
given experiment.This follows
mathematically from the fact that the laws of quantum theory are for the
phenomena in which Planck’s constant can be considered as a very
small quantity, approximately identical with the classical laws.But it would be a mistake to believe that this application of
the quantum-theoretical laws to the measuring device could help to avoid the
fundamental paradox of quantum
theory.The
measuring device deserves this name only if it is in close contact
with the rest of the world, if there is an interaction between the device
and the observer.Therefore, the uncertainty with
respect to the microscopic behavior of the world will enter into the
quantum-theoretical system here just as well as in the first interpretation.If the measuring device would be isolated from the rest of the world,
it would be neither a measuring device nor could it be described in the
terms of classical physics at all.

With
regard to this situation Bohr has emphasized that it is more realistic to
state that the division into the object and the rest of the world is not
arbitrary.Our actual situation
in research work in atomic physics is usually this: we wish to understand a certain
phenomenon, we wish to recognize how this phenomenon
follows from the general laws of nature.Therefore, that part of matter or radiation which takes part
in the phenomenon is the natural object in the theoretical treatment
and should be separated in this respect from the tools used to study the
phenomenon.This again
emphasizes a subjective element in the
description of atomic events, since the measuring device has been
constructed by the observer, and we have to remember that what we observe is
not nature in itself but nature exposed to our method of questioning.Our scientific work in physics consists in asking questions about
nature in the language that we possess and trying to get an answer from
experiment by the means that are
at our disposal.In this way
quantum theory reminds us, as Bohr
has put it, of the old wisdom that when searching for harmony in life one must never forget that in the drama of existence
we are ourselves both players and spectators.It is understandable that in our scientific relation to nature our
own activity becomes very important when we have to deal with parts
of nature into which we can penetrate only by using the most
elaborate tools.

A
company of chessmen stand on the same squares as where we left them—although
perhaps the chessboard has, in the meantime, been carried out of the room
into another.

—John
Locke

When
we combine quantum theory and relativity, there seems to be the possibility
that space and time might form a finite, four-dimensional continuum without
singularities or boundaries.If
we do discover a complete theory of everything, it should be understandable
by everyone and not just a few scientists.Then we shall all, philosophers, scientists and ordinary people, be
able to take part in discussing questions as to why both we and the universe
exist.If we find the answer to
that it would be the ultimate triumph of human reason—for then we would at
last know the mind of God.

Throughout
the history of science new discoveries and new ideas have always caused scientific disputes, have led to polemical
publications criticizing the new ideas, and such criticism
has often been helpful in their development; but these controversies
have never before reached that degree of violence which they attained after
the discovery of the theory of relativity and in a lesser degree after
quantum theory.In both cases
the scientific problems have finally become connected with political issues;
and some scientists have taken recourse to political methods
to carry their views through.This
violent reaction on the recent
development of modern physics can only be understood when one realizes that here the foundations of physics have
started moving; and that this motion has caused the feeling that the
ground would be cut from science.At
the same time it probably means that one has not yet found the
correct language with which to speak about the new situation and that the
incorrect statements published here and there in the enthusiasm about the new
discoveries have caused all kinds of misunderstanding.This is indeed a
fundamental problem.The
improved experimental technique of our time brings into the scope of
science new aspects of nature which
cannot be described in terms of the common
concepts.But in what language,
then, should they be described?The first language that emerges from the process of scientific
clarification is in theoretical physics usually a mathematical
language, the mathematical scheme, which allows one to predict the results
of experiments.The physicist
may be satisfied when he has the mathematical scheme and knows how to use
it for the interpretation of the experiments.But he has to speak about
his results also to nonphysicists who will not be satisfied unless some
explanation is given in plain language, understandable to anybody.Even for the physicist the description in plain language will be a criterion of the degree of understanding that
has been reached.To what
extent is such a description at all
possible?Can one speak about
the atom itself?This is a problem
of language as much as of physics, and therefore some remarks
are necessary concerning language in general and scientific language
specifically.

Language
was formed during the prehistoric age among the human race as a means for communication and as a basis for thinking.We know little about the various steps in its formation; but
language now contains a great number of concepts which are
a suitable tool for more or less unambiguous communication about
events in daily life.These
concepts are acquired gradually without critical analysis by using the
language, and after having used
a word sufficiently often we think that we more or less know what it means.It is of
course a well-known fact that the words
are not so clearly defined as they seem to be at first sight and
that they have only a limited range of applicability.For instance, we can
speak about a piece of iron or a piece of wood, but we cannot speak about a
piece of water.The word
“piece” does not apply to
liquid substances.Or, to
mention another ex­ample: In discussions about the limitations of concepts,
Bohr likes to tell the
following story: “A little boy goes into a grocer’s shop with a
penny in his hand and asks—Could I have a penny’s
worth of mixed sweets?The
grocer takes two sweets and hands them to the boy saying: ‘Here you have
two sweets. You can do the mixing yourself.’ “ A more serious example of
the problematic relation between words and concepts is the fact that
the words “red” and “green” are used even by people who are
colorblind, though the ranges of applicability of these terms must
be quite different for them from what they are for other people.

This
intrinsic uncertainty of the meaning of words was of course recognized very early and has brought about the need for
definitions, or—as
the word “definition” says—for
the setting of boundaries
that determine where the word is to be used and where not.But definitions
can be given only with the help of other
concepts, and so one will finally have to rely on some concepts
that are taken as they are, unanalyzed and undefined.In Greek philosophy the problem of the concepts in language has
been a major theme since Socrates, whose life was—if we can
follow Plato’s artistic representation in his dialogues—a continuous
discussion about the content of the concepts in language and about the
limitations in modes of expression.In
order to obtain a solid basis for scientific thinking, Aristotle in his
logic started to analyze the forms of language, the formal structure of
conclusions and deductions independent of their content.In this way he
reached a degree of abstraction and precision that had been
unknown up to that time in Greek philosophy and he thereby
contributed immensely to the clarification, to the establishment
of order in our methods of thought.He
actually created the basis for the scientific language.

On
the other hand, this logical
analysis of language again involves the danger of an
oversimplification.In logic
the attention is drawn to very special structures, unambiguous connec­tions
between premises and deductions, simple patterns of reasoning, and all the other structures of language are neglected.These other
structures may arise from associations between certain meanings of
words; for instance, a secondary meaning of a word which passes only vaguely through the mind when the word is heard
may contribute essentially to the content of a sentence.The fact that
every word may cause many only half-conscious
movements in our mind can be used to represent some part
of reality in the language much more clearly than by the use
of the logical patterns.Therefore,
the poets have often objected to this emphasis in language and in thinking
on the logical pattern, which-if I interpret their opinions correctly—can make
language less suitable for its purpose.We may recall for instance the words in Goethe’s Faust which
Mephistopheles speaks to the young student:

Waste
not your time, so fast it flies;

Method
will teach you time to win;

Hence,
my young friend, I would advise,

With
college logic to begin.

Then
will your mind be so well braced,

In
Spanish boots so tightly laced,

That
on twill circumspectly creep,

Thought’s
beaten track securely keep,

Nor
will it, ignis-fatuus like,

Into
the path of error strike.

Then
many a day they’ll teach you how

The
mind’s spontaneous acts, till now

As
eating and as drinking free,

Require
a process;—one, two, three!

In
truth the subtle web of thought

Is
like the weaver’s fabric wrought,

One
treadle moves a thousand lines,

Swift
dart the shuttles to and fro,

Unseen
the threads unnumbered flow,

A
thousand knots one stroke combines.

Then
forward steps your sage to show,

And
prove to you it must be so;

The
first being so, and so the second.

The
third and fourth deduced we see;

And
if there were no first and second,

Nor
third nor fourth would ever be.

This,
scholars of all countries prize,

Yet
among themselves no weavers rise.

Who
would describe and study aught alive,

Seeks
first the living spirit thence to drive:

Then
are the lifeless fragments in his hand,

There
only fails, alas I—the
spirit—band.

This
passage contains an admirable description of
the structure of language
and of the narrowness of the simple logical patterns.On the other hand,
science must be based upon language as the only means of communication and
there, where the problem of
unambiguity is of greatest importance, the logical patterns must
play their role.The
characteristic difficulty at this point may be described in the following
way.In natural science we try to
derive the particular from the general, to understand the par­ticular
phenomenon as caused by simple general laws.The general laws when formulated in the language can contain only a
few simple concepts—else
the law would not be simple and general.From these concepts are derived an infinite variety of possible
phenomena, not only qualitatively but with complete precision with respect
to every detail.It is obvious
that the concepts of ordinary language, inaccurate and only vaguely defined
as they are, could never allow such derivations.When a chain of conclusions follows from given premises, the number of possible
links in the chain depends on the precision of the premises.Therefore, the concepts of the general laws must in natural science
be defined with complete precision, and this can be achieved only by means
of mathematical abstraction.In other sciences the situation may be somewhat similar in so
far as rather precise definitions are also required; for instance, in law.But here the number of links in the chain of conclusions need not be
very great, complete precision is not needed, and rather precise definitions
in terms of ordinary language are sufficient.

In
theoretical physics we try to understand groups of phenomena by introducing mathematical symbols that can be correlated with
facts, namely, with the results of measurements.For the
symbols we use names that visualize their correlation with the measurement.Thus
the symbols are attached to the language.Then the symbols are interconnected by a rigorous system of
definitions and axioms, and finally the natural laws are expressed
as equations between the symbols.The
infinite variety of solutions of these equations then corresponds to
the infinite variety of particular phenomena that are possible in this part
of nature.In this way the
mathematical scheme represents the group
of phenomena so far as the correlation between the symbols and the
measurements goes.It is this
correlation which permits the
expression of natural laws in the terms of common language, since our
experiments consisting of actions and observations can always be described
in ordinary language.

Still
in the process of expansion of scientific knowledge the language also
expands; new terms are introduced and the old ones are applied in a wider
field or differently from ordinary language.Terms such as energy, electricity and entropy are obvious examples.In this way we develop a scientific language which may be called a natural extension of ordinary language adapted to
the added fields of scientific knowledge.During the past century a number of new concepts have been introduced
in physics, and in some cases it has taken considerable
time before the scientists have really grown accustomed to their
use.The term electromagnetic
field, for instance, which was to some extent already present in Faraday’s
work and which later formed the basis of Maxwell’s theory, was not easily
accepted by the physicists, who directed their attention primarily to
the mechanical motion of matter.The
introduction of the concept really involved a change in scientific
ideas as well, and such changes are not easily accomplished.

Still,
all the concepts introduced up to the end of the last century formed a
perfectly consistent set applicable to a wide field of experience, and,
together with the former concepts, formed a language which not only the
scientists but also the technicians and engineers could successfully apply
in their work.To
the underlying fundamental ideas of this language belonged the
assumptions that the order of events in time is entirely independent of
their order in space, that Euclidean geometry is valid in real space, and
that the events “happen” in space and time
independently of whether they are observed or not.It was not denied that
every observation had some influence on the phenomenon
to be observed but it was generally assumed that by doing the experiments cautiously this influence could be made arbitrarily
small.This seemed in fact a necessary condition for the ideal of
objectivity which was considered as the basis of all natural
science.

Into
this rather peaceful state of physics broke quantum theory and the theory of special relativity as a sudden, at first slow
and then gradually increasing, movement in the foundations
of natural science.The first
violent discussions developed around
the problems of space and time raised by the theory of relativity.How should one
speak about the new situation?Should
one consider the Lorentz contraction of moving bodies as a real
contraction or only as an apparent contraction?Should one say that the structure of space and time was really
different from what it had been assumed to be or should one only say that
the experimental results could be connected mathematically in a way
corresponding to this new structure, while space and time, being the
universal and necessary mode in which things appear to us, remain what they
had always been?The real
problem behind these many
controversies was the fact that no language existed in which one
could speak consistently about the new situation.The ordinary language was based upon the old concepts of space and
time and this language offered the only unambiguous means of communication
about the setting up and the
results of the measurements.Yet
the experiments showed that
the old concepts could not be applied everywhere.

The
obvious starting point for the interpretation of the theory of relativity
was therefore the fact that in the limiting.case of small velocities (small compared with the velocity of light)
the new theory was practically identical with the old one.Therefore, in this
part of the theory it was obvious in which way the mathematical
symbols had to be correlated with the measurements and with the terms of
ordinary language; actually it was only through this correlation that the
Lorentz transformation had been found.There was no ambiguity about the meaning of the words and the symbols
in this region.In fact this
correlation was already sufficient for the application of the theory to the
whole field of experimental research connected with the problem of
relativity.Therefore, the
controversial questions about the “real” or the “apparent” Lorentz
contraction, or about the definition of
the word “simultaneous” etc., did not concern the facts but rather
the language.

With
regard to the language, on the other hand, one has gradually recognized that
one should perhaps not insist too much on certain principles.It is always difficult to find general convincing criteria for which
terms should be used in the language and how they should be used.One should simply wait for the development of the language, which
adjusts itself after some time to the new situation.Actually in the theory of special relativity this adjustment has
already taken place to a large extent during
the past fifty years.The
distinction between “real” and “apparent”
contraction, for instance, has simply disappeared.The word
“simultaneous” is used in line with the definition given by
Einstein, while for the wider definition discussed in an earlier chapter the
term “at a space-like distance” is commonly used, etc.

In
the theory of general relativity the idea of a non-Euclidean geometry
in real space was strongly contradicted by some philosophers who pointed out that our whole method of setting up the
experiments already presupposed Euclidean geometry.In fact if a
mechanic tries to prepare a perfectly plane surface, he
can do it in the following way.He
first prepares three surfaces of,
roughly, the same size which are, roughly, plane.Then he tries to
bring any two of the three surfaces into contact by putting
them against each other in different relative positions.The degree to which this contact is possible on the
whole surface is a measure of the degree of accuracy with which the surfaces
can be called “plane.” He will
be satisfied with his three surfaces only if the contact between any two of
them is complete everywhere.If
this happens one can prove mathematically that Euclidean geometry holds on
the three surfaces.In this
way, it was argued, Euclidean
geometry is just made correct by our own measures.

From
the point of view of general relativity, of course, one can answer that this
argument proves the validity of Euclidean geometry
only in small dimensions, in the dimensions of our experimental
equipment.The accuracy with
which it holds in this region
is so high that the above process for getting plane surfaces can
always be carried out.The
extremely slight deviations from Euclidean
geometry which still exist in this region will not be realized since
the surfaces are made of material which is not strictly rigid but allows for
very small deformations and since the concept of “contact” cannot be
defined with complete precision.For
surfaces on a cosmic scale the process that has been described would just
not work; but this is not a problem of experimental physics.

Again,
the obvious starting point for the physical interpretation of the
mathematical scheme in general relativity is the fact that the geometry is
very nearly Euclidean in small dimensions; the
theory approaches the classical theory in this region.Therefore, here the correlation between the mathematical
symbols and the measurements and the concepts in ordinary language is
unambiguous.Still, one can
speak about a non-Euclidean geometry in large dimensions. In
fact a long time before the theory of general relativity had even been
developed the possibility of a non-Euclidean
geometry in real space seems to have been con­sidered by the
mathematicians, especially by Gauss in Göttingen.When he carried out very accurate geodetic measurements on a triangle
formed by three mountains—the Brocken in the Harz Mountains, the Inselberg
in Thuringia, and the Hohenhagen near Göttingen—he is said to have
checked very carefully whether the
sum of the three angles was actually equal to 180 degrees; and that
he considered a difference which would prove deviations from Euclidean
geometry as being possible.Actually
he did not find any deviations within his accuracy of measurement.In the theory of
general relativity the language by which we describe
the general laws actually now follows the scientific language of the
mathematicians, and for the description of the experiments
themselves we can use the ordinary concepts, since Euclidean
geometry is valid with sufficient accuracy in small dimensions.

The
most difficult problem, however, concerning the use of the language arises
in quantum theory.Here we have
at first no simple guide for
correlating the mathematical symbols with concepts
of ordinary language; and the only thing we know from the
start is the fact that our common concepts cannot be applied to the
structure of the atoms.Again the obvious starting point for the physical
interpretation of the formalism seems to be the fact that the mathematical
scheme of quantum mechanics approaches that of classical mechanics in
dimensions which are large as compared to the size of the atoms.But even this statement must
be made with some reservations.Even
in large dimensions there are many solutions of the quantum-theoretical
equations to which no analogous solutions can be found in classical
physics.In these solutions the
phenomenon of the interference of probabilities
would show up, as was discussed in the earlier chapters; it does not
exist in classical physics.Therefore,
even in the limit of large dimensions the correlation between the
mathematical symbols, the measurements, and the ordinary concepts is by
no means trivial.In order to
get to such an unambiguous correlation
one must take another feature of the problem into account.It must be observed that the system which is treated by the
methods of quantum mechanics is in fact a part of a much bigger system
(eventually the whole world); it is interacting with this bigger system; and
one must add that the microscopic properties of the bigger system are (at
least to a large extent) unknown.This
statement is undoubtedly a correct description of the actual situation.Since the system could not be the object of measurements and of
theoretical investigations, it would in fact not belong to the world of
phenomena if it had no interactions with such a bigger system of which the
observer is a part.The
interaction with the bigger system with its undefined microscopic properties
then introduces a new statistical element into the description-both the
quantum-theoretical and the classical one-of the system under consideration.In the limiting case of the large dimensions this statistical element
destroys the effects of the “interference of probabilities” in such a
manner that now the quantum-mechanical scheme really approaches the
classical one in the limit.Therefore,
at this point the correlation between the mathematical symbols of quantum
theory and the concepts of ordinary
language is unambiguous, and this correlation suffices
for the interpretation of the experiments.The remaining problems
again concern the language rather than the facts, since it
belongs to the concept “fact” that it can be described in ordinary
language.

But
the problems of language here are really serious.We wish to speak in some way about the structure of the atoms and not
only about the
“facts”—the latter being, for instance, the black spots on a
photographic plate or the water droplets in a cloud chamber.But we cannot speak about the atoms in ordinary language.The analysis can now
be carried further in two entirely different ways.We can either ask which language concerning the atoms
has actually developed among the physicists in the thirty years
that have elapsed since the formulation of quantum mechanics.Or we can describe the attempts for defining a precise scientific
language that corresponds to the mathematical scheme.

In
answer to the first question one may say that the concept of complementary
introduced by Bohr into the interpretation of
quantum theory has encouraged the physicists to use an ambiguous
rather than an unambiguous language, to use the classical concepts in a
somewhat vague manner in conformity with the
principle of uncertainty, to apply alternatively different classical
concepts which would lead to contradictions if used simultaneously.In this way one speaks about electronic orbits, about matter
waves and charge density, about energy and momentum, etc., always conscious
of the fact that these concepts have only a very limited range of
applicability.When this vague
and unsystematic use of the language leads into difficulties, the physicist
has to withdraw into the mathematical scheme and its unambiguous correlation
with the experimental facts.

This
use of the language is in many ways quite satisfactory, since it
reminds us of a similar use of the language in daily life or
in poetry.We realize that the
situation of complementary is not
confined to the atomic world alone; we meet it when we reflect
about a decision and the motives for our decision or when we have the choice
between enjoying music and analyzing its structure.On the other hand, when the classical concepts are used in
this manner, they always retain a certain vagueness, they acquire in their
relation to “reality” only the same statistical significance as the
concepts of classical thermodynamics in its statistical interpretation.Therefore, a short discussion of these statistical
concepts of thermodynamics may be useful.

The
concept temperature in classical thermodynamics seems
to describe an objective feature of reality, an objective property of
matter.In daily life it is
quite easy to define with the help
of a thermometer what we mean by stating that a piece of matter
has a certain temperature.But
when we try to define what
the temperature of an atom could mean we are, even in classical physics, in
a much more difficult position.Actually
we cannot correlate this concept “temperature of the atom” with a
well-defined property of the atom but have to connect it at least partly
with our insufficient knowledge of it.We can correlate the
value of the temperature with certain statistical expectations about the
properties of the atom, but it seems rather doubtful whether an expectation
should be called objective.The
concept “temperature of the atom” is not much better defined than the
concept “mixing” in the story about the boy who bought mixed sweets.

In
a similar way in quantum theory all the classical concepts are, when applied to the atom, just as well and just as little defined
as the “temperature of the atom;” they are correlated with
statistical expectations; only in rare cases may the expectation
become the equivalent of certainty.Again,
as in classical thermodynamics, it is difficult to call the expectation
objective.One might perhaps
call it an objective tendency or possibility, a “potentia” in the sense
of Aristotelian philosophy.In
fact, I believe that the language
actually used by physicists when they speak
about atomic events produces in their minds similar notions as the concept “potentia.” So the physicists have gradually
become accustomed to considering the electronic orbits, for
example, not as reality but rather as a kind of “potentia.” The language
has already adjusted itself, at least to some extent, to this
true situation.But it is not a
precise language in which one could use the normal logical patterns;
it is a language that produces pictures in our mind, but together with them
the notion that the pictures have only a vague connection with reality, that
they represent only a tendency toward reality.

The
vagueness of this language in use among the physicists has therefore led to
attempts to define a different precise language which
follows definite logical patterns in complete conformity with
the mathematical scheme of quantum theory.The result of these
attempts by Birkhoff and Neumann and more recently by Weizsacker can
be stated by saying that the mathematical scheme
of quantum theory can be interpreted as an extension or modification
of classical logic.It is
especially one fundamental principle of classical logic which seems to
require a modification.In
classical logic it is assumed that, if a statement has any meaning at all,
either the statement or the negation of the statement must
be correct.Of “here is a
table” or “here is not a table,” either
the first or the second statement must be correct.Tertium non datur, a third possibility does not exist.It may be that we do
not know whether the statement or its negation is correct; but in
“reality” one of the two is correct.

In
quantum theory this law tertium non datur is to be modified.Against any modification of this fundamental principle one can of
course at once argue that the principle is assumed in common
language and that we have to speak at least about our eventual
modification of logic in the natural language.Therefore, it would be a self-contradiction to describe in natural language
a logical scheme that does not apply to natural language.There, however, Weizsacker points out that one may distinguish
various levels of language.One level refers to the objects-for instance, to the atoms or
the electrons.A second level refers to statements about objects.A third level may refer
to statements about statements about objects, etc.It would then be possible to have different logical patterns
at the different levels.It is
true that finally we have to go back to the natural language and
thereby to the classical logical
patterns.But Weizsacker
suggests that classical logic may be in a similar manner a priori to
quantum logic, as classical physics is to quantum theory.Classical logic would then be contained as a kind of limiting case in
quantum logic, but the latter would
constitute the more general logical pattern.

The
possible modification of the classical logical pattern shall, then,
first refer to the level concerning the objects.Let us consider an atom moving in a closed box which is divided by a
wall into two equal parts.The wall may have a very small hole so that
the atom can go through.Then
the atom can, according to classical
logic, be either in the left half of the box or in the right half.There is no third possibility: “tertium non datur.” In quantum theory, however, we have to admit—if we use the words
“atom” and “box” at all—that there are other possibilities which
are in a strange way mixtures of the two former possibilities.This is necessary for explaining the results of our experiments.We could, for instance, observe light that has been scattered by the
atom.We could perform three
experiments—first the atom is (for instance, by closing the hole in the
wall) confined to the left
half of the box, and the intensity distribution of the scattered light is
measured; then it is confined to the right half and again the scattered
light is measured; and finally the atom can move freely in the whole
box and again the intensity distribution of the scattered light is measured.If the atom would always be in either the left half or the right half
of the box, the final intensity distribution should be a mixture (according
to the fraction of time spent by
the atom in each of the two parts) of the two former intensity
distributions.But this is in
general not true
experimentally.The real
intensity distribution is modified by the
“interference of probabilities”; this has been discussed before.

In
order to cope with this situation Weizsacker has introduced the
concept “degree of truth.” For any simple statement in an alternative
like “The atom is in the left (or in the right) half of the
box” a complex number is defined as a measure for its “degree of
truth.” If the number is one, it means that the statement is true; if the
number is zero, it means that it is false.But other values are possible.The
absolute square of the complex number gives the probability for the
statement’s being true; the sum of the two probabilities referring to the
two parts in the alternative (either
left or right in our case) must be unity.But each pair of
complex numbers referring to the two parts of the alternative
represents, according to Weizsacker’s definitions, a “statement”
which is certainly true if the numbers have just these
values; the two numbers, for instance, are sufficient for determining
the intensity distribution of scattered light in our experiment.If one allows the use of the term “statement” in this way one can
introduce the term “complementary” by the following definition—Each
statement that is not identical with either
of the two alternative statements—in our case with the statements: “the atom is in the left half” or “the atom is in the right
half of the box”—is called
complementary to these statements.For
each complementary statement the question whether the atom is left or right is not decided.But the term “not decided is by no means equivalent to the
term “not known.““Not
known” would mean that the atom is “really” left or right, only we do not know where it is.But
“not decided” indicates a different situation, expressible only by a complementary statement.

This
general logical pattern, the details of which cannot be described here,
corresponds precisely to the mathematical formalism
of quantum theory.It forms the
basis of a precise language that can be used to describe the
structure of the atom.But the
application of such a language raises a number of difficult
problems of which we shall discuss only two here: the relation between the different “levels” of language and the consequences
for the underlying ontology.In
classical logic the relation between the different levels of language is a one-to-one correspondence.The two statements, “The
atom is in the left half” and “It is true that the atom is in the
left half,” belong logically to different levels.In classical logic these statements are completely equivalent, for
instance, they are either both true or both false.It is not possible that the one is true and the
other false.But in the logical
pattern of complementary this relation is more complicated.The correctness or incorrectness of the first
statement still implies the correctness or incorrectness of the second
statement.But the
incorrectness of the second statement
does not imply the incorrectness of the first statement.If the second statement
is incorrect, it may be undecided whether the
atom is in the left half; the atom need not necessarily be in the
right half.There is still complete equivalence between the two
levels of language with respect to the correctness of a statement,
but not with respect to the incorrectness.From this connection one can understand the persistence of the
classical laws in quantum theory: wherever a definite result can be derived
in a given experiment by the application of the classical laws the result
will also follow from quantum theory, and it will hold experimentally.

The
final aim of Weizsacker’s attempt is to apply the modified logical patterns also in the higher levels of language, but these
questions cannot be discussed here.The
other problem concerns the ontology that underlies the modified
logical patterns.If the pair of complex numbers represents a “statement”
in the sense just described, there should exist a
“state” or a “situation” in nature in which the statement is correct.We will use the word “state” in this connection.The “states” corresponding to complementary statements are then called
“coexistent states” by Weizsacker.This term “coexistent” describes
the situation correctly; it would in fact be difficult to call them
“different states,” since every state contains to some extent also the
other “coexistent states.” This concept of “state” would then form a
first definition concerning the ontology of quantum
theory.One sees at once that
this use of the word “state,”
especially the term “coexistent state,” is so different from the usual
materialistic ontology that one may doubt whether
one is using a convenient terminology.On the other hand, if
one considers the word “state” as describing some potentiality
rather than a reality—one
may even simply replace the term “state” by the term
“potentiality”—then the concept of “coexistent
potentialities” is quite plausible, since one potentiality may involve or
overlap other potentialities.

All
these difficult definitions and distinctions can be avoided if one
confines the language to the description of facts, ie. experimental results.However, if one wishes to speak about the atomic particles themselves
one must either use the mathematical scheme as the only supplement to
natural language or one must combine it with a language that makes use of a
modified logic or of no well-defined logic at all.In the experiments about atomic
events we have to do with things and facts, with phenomena that are
just as real as any phenomena in daily life.But the atoms or the elementary particles themselves are not as real;
they form a world of potentialities or possibilities rather than one of
things or facts.

The
philosophical implications of modern physics have been discussed in
the foregoing chapters in order to show that this most modern part of
science touches very old trends of thought at
many points, that it approaches some of the very old problems from a new direction.It is
probably true quite generally that in the history of human thinking the most fruitful developments frequency
take place at those points where two different lines of thought meet.These lines may have their roots in quite different parts of
human culture, in different times or different cultural environments or
different religious traditions; hence if they actually meet, that is, if they are at least so much related to each other
that a real interaction can take place, then one may hope that
new and interesting developments will follow.Atomic physics as a part of modem science does actually
penetrate in our time into very different cultural traditions.It is not only taught in
Europe and the Western countries, where it.belongs to the traditional
activity in the natural sciences, but it is also studied in the Far East, in
countries like Japan and China and India.

While
nineteenth-century psychology was busy at work analyzing the conscious mind,
psychoanalysis was engaged in explorations of the unconscious mind.Freud felt that consciousness was only a thin slice of the total
mind, that like an iceberg, the larger part of it existed below the surface
of awareness.Psychologists
answered Freud by saying that the notion of an unconscious mind was a
contradiction in terms; the mind, by definition, was conscious.The controversy never reached a final conclusion because both
psychology and psychoanalysis changed their objective during the twentieth
century.Psychology became the
science of behavior and psychoanalysis became the science of personality.

The
philosophical implications of modern physics have been discussed in
the foregoing chapters in order to show that this most modern part of
science touches very old trends of thought at
many points, that it approaches some of the very old problems from a new direction.It is
probably true quite generally that in the history of human thinking the most fruitful developments frequency
take place at those points where two different lines of thought meet.These lines may have their roots in quite different parts of
human culture, in different times or different cultural environments or
different religious traditions; hence if they actually meet, that is, if they are at least so much related to each other
that a real interaction can take place, then one may hope that
new and interesting developments will follow.Atomic physics as a part of modem science does actually
penetrate in our time into very different cultural traditions.It is not only taught in
Europe and the Western countries, where it belongs to the traditional
activity in the natural sciences, but it is also studied in the Far East, in
countries like Japan and China and India, with their quite different
cultural background, and in Russia, where
a new way of thinking has been established in our time; a
new way related
both to specific scientific developments of the Europe of the nineteenth
century and to other entirely different traditions
from Russia itself.It can
certainly not be the purpose of the following discussion to make
predictions about the probable result of the encounter between the ideas of
modern physics and the older
traditions.But it may be
possible to define the points from which the interaction between the
different ideas may begin.

In
considering this process of expansion of modern physics it would certainly
not be possible to separate it from the general expansion of natural
science, of industry and engineering, of medicine, etc., that is, quite
generally of modern civilization in all
parts of the world.Modern
physics is just one link in a long chain of events that started from
the work of Bacon, Galileo and Kepler and from the practical application of
natural science in the seventeenth and eighteenth centuries.The connection between
natural science and technical science has from the beginning been
that of mutual
assistance: The progress in
technical science, the improvement of the tools, the invention of new
technical devices have provided the basis for more, and more accurate,
empirical knowledge of nature; and the progress in the understanding of
nature and finally the mathematical formulation of natural laws have opened
the way to new applications of this knowledge in technical science.For instance, the invention of the telescope enabled the astronomers
to measure the motion of the stars more accurately than before; thereby a
considerable progress in astronomy
and in mechanics was made possible.On the other hand, precise knowledge of the mechanical laws
was of the greatest value for the improvement of mechanical tools, for
the construction of engines, etc.The
great expansion of this combination of natural and technical science started
when one had
succeeded in putting some of the forces of nature at the disposal
of man.The energy stored up in
coal, for instance, could then perform some of the work which formerly had to be
done by
man himself.The industries
growing out of these new possibilities could first be considered as a natural
continuation and expansion
of the older trades; at many points the work of the machines still resembled
the older handicraft and the work in the chemical factories could
be considered as a continuation of the work in the dyehouses and the
pharmacies of the older times.But
later entirely new branches of industry developed which had no
counterpart in the older trades; for instance, electrical engineering.The penetration of science into the more remote parts of nature
enabled the engineers to use forces of nature which in former
periods had scarcely been
known; and the accurate knowledge
of these forces in terms of a mathematical formulation
of the laws governing them formed a solid basis for the construction of
all kinds of machinery.

The
enormous success of this combination of natural and technical science led to a strong preponderance of those
nations or states or
communities in
which this kind of human
activity flourished, and as a natural consequence this activity had
to be taken up even by those nations which by tradition would not have
been inclined toward natural and technical sciences.The modern means of
communication and of traffic finally completed this process of
expansion of technical civilization.Undoubtedly
the process has fundamentally changed the conditions of life on our earth;
and whether one approves of it or not, whether one calls it progress or
danger, one must realize that it has gone far beyond any control through
human forces.One may
rather consider it as a biological process on the largest scale whereby
the structures active in the human organism encroach on larger parts
of matter and transform it into a state suited for the
increasing human population.

Modern
physics belongs to the most recent parts of this development, and its
unfortunately most visible result, the invention
of nuclear weapons, has shown the essence of this development
in the sharpest possible light.On
the one hand, it has demonstrated
most clearly that the changes brought about by the combination of natural
and technical sciences cannot be looked at only from the optimistic
viewpoint; it has at least partly justified the views of those who had
always warned against the dangers of such radical transmutation of our
natural conditions of life.On the other hand, it has compelled even those
nations or individuals who tried to keep apart from these dangers
to pay the strongest attention to the new development, since
obviously political power in the sense of military power rests upon the
possession of atomic weapons.It
can certainly not be the task of
this volume to discuss extensively the political implications of nuclear
physics.But at least a few
words may be said about these problems because they always come first into
the minds of people when
atomic physics is mentioned.

It
is obvious that the invention of the new weapons, especially of the
thermonuclear weapons, has fundamentally changed the political structure of
the world.Not only has the
concept of independent nations or states undergone a decisive change, since
any nation which is not in possession of such weapons must depend in
some way on those very few nations that do produce these arms
in large quantity; but also the attempt of warfare on a large scale
by means of such weapons has become practically an absurd kind of suicide.Hence one frequently hears the optimistic view
that therefore war has become obsolete, that it will not happen again.This view, unfortunately, is a much too optimistic
oversimplification.On the
contrary, the absurdity of warfare by means
of thermonuclear weapons may, in a first approximation, act as an
incentive for war on a small scale.Any
nation or political group which is convinced of its historical or moral
right to enforce some change of the present situation will feel that the use
of conventional arms for this purpose will not involve any great risks; they
will assume that the other side will certainly not have recourse to
the nuclear weapons, since the other side being historically and morally wrong in this issue will not take the chance
of war on a large scale.This
situation would in turn induce
the other nations to state that in case of small wars inflicted upon
them by aggressors, they would actually have recourse to the nuclear
weapons, and thus the danger obviously remains.It may quite well be that in about twenty or thirty years from now
the world will have undergone so great changes that the danger of warfare on a large scale, of the application of all
technical resources for the annihilation of the opponent, will have
greatly diminished or disappeared.But
the way to this new state will be full of the greatest dangers.We must as in all former times, realize that what looks
historically or morally right to the one side may look wrong to the other
side.The continuation of the status quo may not always be the
correct solution; it may, on the contrary, be most important to find
peaceful means of adjustments to new situations, and it may in many cases be
extremely difficult to find any just decision at all.Therefore, it is probably not
too pessimistic to say that the Great War can be avoided only if all
the different political groups are ready to renounce
some of their apparently most obvious rights—in
view of the fact that the question of right or wrong may look essentially
different from the other side.This
is certainly not a new point
of view; it is in fact only an application of that human attitude
which has been taught through many centuries by some of
the great religions.

The
invention of nuclear weapons has also raised entirely new problems for science and scientists.The political influence of science
has become very much stronger than it was before World War II, and
this fact has burdened the scientist, especially the atomic physicist, with a double responsibility.He can either take an active part in the administration of the
country in connection with the importance of science for the community; then
he will eventually have to face the
responsibility for decisions of enormous weight which go far beyond the
small circle of research and university work to which he was wont.Or he may voluntarily
withdraw from any participation in political decisions;
then he will still be responsible for wrong decisions which he could possibly have prevented had he not preferred the quiet
life of the scientist.Obviously
it is the duty of the scientists to
inform their governments in detail about the unprecedented destruction
that would follow from a war with thermonuclear weapons.Beyond that, scientists are frequently requested to participate in
solemn resolutions in favor of world peace; but considering this latter
demand I must confess that I have never been able to see any point in
declarations of this kind.Such
resolutions may seem a welcome proof of goodwill; but anyone who speaks in
favor of peace without stating precisely the conditions of this peace must
at once be suspected of speaking only about that kind of peace in which he
and his group thrive best-which of course
would be completely worthless.Any
honest declaration for peace
must be an enumeration of the sacrifices one is prepared to make for its
preservation.But as a rule the
scientists have no authority
to make statements of this kind.

At
the same time the scientist can do his best to promote international co-operation in his own field.The great importance that
many governments attach to research in nuclear physics nowadays and
the fact that the level of scientific work is still very different in
different countries favors international cooperation in this work.Young scientists of many different countries may gather in research
institutions in which a strong activity in the field of modern physics is
going on and the common work on difficult scientific problems will foster
mutual understanding.In one
case, that of the Geneva organization, it has even been possible
to reach an agreement between a number of different nations for building a
common laboratory and for constructing by a combined effort the expensive
experimental equipment for research
in nuclear physics.This kind
of cooperation will certainly help
to establish a common attitude toward the problems of science—common even
beyond the purely scientific problems among the younger generation of scientists.Of course one does not
know beforehand what will grow out of the seeds that have been
sown in this way when the scientists return into their old environments
and again take part in their own cultural traditions.But one can scarcely doubt that the exchange of ideas between young
scientists of different countries and between the different generations in
every country will help to approach without too much tension that new state
of affairs in which a balance is reached between the older traditional
forces and the inevitable necessities of modern life.It is especially one feature of science which makes it more than
anything else suited for establishing the first strong connection between
different cultural traditions.This is the fact that the ultimate decisions about the value of
a special scientific work, about what is correct or wrong in the work,
do not depend on any human authority.It
may sometimes take many
years before one knows the solution of a problem, before
one can distinguish between truth and error; but finally the
questions will be decided, and the decisions are made not by any
group of scientists but by nature itself.Therefore, scientific ideas spread among those who are interested in
science in an entirely different way from the propagation of political ideas.

While
political ideas may gain a convincing influence among great masses of people
just because they correspond or seem to correspond to the prevailing
interests of the people, scientific ideas will spread only because they are true.There are objective and final criteria assuring the
correctness of a scientific statement.All that has here been said
about international cooperation and exchange of ideas would of course
be equally true for any part of modem science; it is by no means confined to
atomic physics.In this respect modem physics is just one of the many branches
of science, and even if its technical applications-the arms and the peaceful
use of atomic energy-attach a special weight to this branch, there would be
no reason for considering international co-operation in this field as far
more important than in any
other field.But we have now to
discuss again those features of modem physics which are essentially
different from the previous development of natural science, and we have for
this purpose once more to go back to the European history of this development that was brought about by the combination of natural
and technical sciences.

It
has frequently been discussed among the historians whether the rise of
natural science after the sixteenth century was in any way
a natural consequence of earlier trends in human thinking.It may be argued that certain trends in Christian philosophy led to a very abstract concept of God, that they put God so far above
the world that one began to consider the world without at the same time also
seeing God in the world.The
Cartesian partition may be called a
final step in this development.Or
one may point out that all the theological controversies of the
sixteenth century produced a general discontent about problems that could
not really be settled by reason and were exposed to the political struggles
of the time; that this discontent favored interest
in problems which were entirely separated from the theological
disputes.Or one may simply
refer to the enormous activity,
the new spirit that had come into the European societies through the
Renaissance.In any case during
this period a new authority
appeared which was completely independent of Christian religion or
philosophy or of the Church, the authority of experience,
of the empirical fact.One may
trace this authority back into older philosophical trends, for
instance, into the philosophy of
Ockham and Duns Scotus, but it became a vital force
of human activity only from the sixteenth century onward.Galileo did not only think about the mechanical
motions, the pendulum and the falling stone; he tried out by experiments, quantitatively,
how these motions took place.This
new activity was in its
beginning certainly not meant as a deviation from the traditional
Christian religion.On the
contrary, one spoke of two kinds of revelation of God.The one was written in the Bible and the other was to be found
in the book of nature.The Holy
Scripture has been written by man
and is therefore subject to error, while nature is the immediate
expression of God’s intentions.

However,
the emphasis on experience was connected with a slow and gradual change in
the aspect of reality.While in the Middle
Ages what we nowadays call the symbolic meaning of a thing was in some way its primary reality, the aspect of reality changed
toward what we can perceive with our senses.What we can see and touch became primarily real.And this new concept of reality could be connected with a new
activity: we can experiment and see how things really are.It was easily seen that this new
attitude meant the departure of the human mind into an immense field of new possibilities, and it can be well understood that
the Church saw in the new movement the dangers rather than the hopes.The famous trial of Galileo in connection with his views on the
Copernican system marked the beginning of a struggle that went on for more
than a century.In this
controversy the representatives of natural science could argue that
experience offers an undisputable truth, that it cannot be left to any human
authority to decide about what really happens in nature, and that this
decision is made by nature or in this sense by God.The representatives of the traditional religion, on the other hand,
could argue that by paying too much attention to the
material world, to what we perceive with our senses, we lose the
connection with the essential values of human life, with just that part of
reality which is beyond the material world.These two arguments do not
meet, and therefore the problem could not be settled by any kind of
agreement or decision.

In
the meantime natural science proceeded to get a clearer and wider picture of
the material world.In physics
this picture was to be described by
means of those concepts which we nowadays call the concepts of
classical physics.The world
consisted of things in space and time, the things consist of matter, and matter
can produce and can be acted upon by forces.The events follow from
the interplay between matter and forces; every event is
the result and the cause of other events.At the same time the human
attitude toward nature changed from a contemplative one to the pragmatic
one.One was not so much
interested in nature as it
is; one rather asked what one could do with it.Therefore, natural science turned into technical science; every advancement of knowledge was connected with the question as to what
practical use could be derived from it.This was true not only
in physics; in chemistry and biology the attitude was essentially the same,
and the success of the new methods in medicine or in agriculture contributed essentially to the propagation of the new
tendencies.

In
this way, finally, the nineteenth century developed an extremely
rigid frame for natural science which formed not only science but
also the general outlook of great masses of people.This frame was supported by
the fundamental concepts of classical
physics, space, time, matter and causality; the concept of reality
applied to the things or events that we could perceive by our senses
or that could be observed by means of the refined tools that technical
science had provided.Matter
was the primary reality.The progress of science was pictured as a crusade of conquest into
the material world.Utility was
the watchword of the time.

On
the other hand, this frame was so narrow and rigid that it was difficult to
find a place in it for many concepts of our language
that had always belonged to its very substance, for instance,
the concepts of mind, of the human soul or of life.Mind could be
introduced into the general picture only as a kind of
mirror of the material world; and when one studied the properties of this mirror in the science of psychology, the scientists
were always tempted—if I may carry the comparison further-to
pay more attention to its mechanical than to its optical properties.Even there one tried to apply the concepts of classical
physics, primarily that of causality.In
the same way life was to be
explained as a physical and chemical process, governed by natural laws, completely determined by causality.Darwin’s concept of evolution provided ample evidence for
this interpretation.It was especially
difficult to find in this framework room for those parts of reality
that had been the object of the traditional religion and seemed now more or
less only imaginary.Therefore, in those European countries in which one was wont to
follow the ideas up to their extreme consequences, an open hostility
of science toward religion developed, and even in the other
countries there was an increasing tendency toward indifference toward
such questions; only the ethical values of the Christian religion were
excepted from this trend, at least for the time being.Confidence in the scientific method and in rational thinking replaced
all other safeguards of the human mind.

Coming
back now to the contributions of modern physics, one may say that the most
important change brought about by its results consists in the dissolution of
this rigid frame of concepts of the
nineteenth century.Of course
many attempts had been made
before to get away from this rigid frame which seemed obviously too
narrow for an understanding of the essential parts of reality.But it had not been possible to see what could
be wrong with the fundamental concepts like matter, space,
time and causality that had been so extremely successful in the
history of science.Only
experimental research itself, carried out with all the refined equipment
that technical science could offer, and its mathematical interpretation,
provided the basis for a critical analysis—or,
one may say, enforced the critical analysis—of
these concepts, and finally resulted in the dissolution of the rigid frame.

This
dissolution took place in two distinct stages.The first was the
discovery, through the theory of relativity, that even such
fundamental concepts as space and time could be changed and in fact must be
changed on account of new experience.This
change did not concern the somewhat vague concepts of space and time in
natural language; but it did concern their precise formulation in the
scientific language of Newtonian mechanics, which had erroneously been
accepted as final.The second
stage was the discussion of the concept of matter enforced by the experimental
results concerning the atomic structure.The idea of the reality of matter had probably been the
strongest part in that rigid frame of concepts of the nineteenth century,
and this idea had at least to be modified in connection with the new ex­perience.Again the concepts so far as they belonged to the natural
language remained untouched.There
was no difficulty in speaking
about matter or about facts or about reality when one
had to describe the atomic experiments and their results.But the scientific extrapolation of these concepts
into the smallest parts of matter could not be done in the simple way
suggested by classical physics, though it had erroneously determined the
general outlook on the problem of matter.

These
new results had first of all to be considered a serious warning
against the somewhat forced application of scientific concepts in domains
where they did not belong.The
application of the concepts of classical physics, eg, in chemistry, had been
a mistake.Therefore, one
will nowadays be less inclined to assume
that the concepts of physics, even those of quantum theory, can
certainly be applied everywhere in biology or other sciences.We will, on the
contrary, try to keep the doors open for the entrance of new concepts even in those parts of science where
the older concepts have been very useful for the understanding
of the phenomena.Especially at
those points where the application
of the older concepts seems somewhat forced or appears not quite adequate to the problem we will try to avoid any
rash conclusions.

Furthermore,
one of the most important features of the development
and the analysis of modem physics is the experience that the concepts
of natural language, vaguely defined as they are, seem to be more stable in
the expansion of knowledge than the precise terms of scientific language,
derived as an idealization from only limited groups of phenomena.This is in fact not surprising since the concepts of natural language
are formed by the immediate connection with reality; they represent reality.It is true that they are not
very well defined and may therefore also undergo changes in the
course of the centuries, just as reality itself did, but they never lose the
immediate connection with reality.On the other hand, the scientific concepts are idealizations;
they are derived from experience obtained by refined experimental tools, and
are precisely defined through axioms and
definitions.Only through these
precise definitions is it possible to connect the concepts with a
mathematical scheme and to derive mathematically the infinite variety of
possible phenomena in this field.But through this process of idealization and precise
definition the immediate connection with reality is lost.The concepts still correspond very closely to reality in that
part of nature which had been the
object of the research.But the
correspondence may be lost in other parts containing other groups of phenomena.

Keeping
in mind the intrinsic stability of the concepts of natural language in the
process of scientific development, one sees
that—after the experience of modem physics—our attitude toward
concepts like mind or the human soul or life or God will be
different from that of the nineteenth century, because these concepts
belong to the natural language and have therefore immediate
connection with reality.It is
true that we will also realize that these concepts are not well
defined in the scientific sense and that their application may lead to
various contradic­tions, for the
time being we may have to take the concepts, unanalyzed
as they are; but still we know that they touch reality.It may be useful in
this connection to remember that even in the most
precise part of science, in mathematics, we cannot avoid using
concepts that involve contradictions.For
instance, it is well known that the concept of infinity leads to
contradictions that have been analyzed, but it would be practically
impossible to construct the main parts of mathematics without this concept.

The
general trend of human thinking in the nineteenth century had been toward an
increasing confidence in the scientific method and in precise rational
terms, and had led to a general skepticism with regard to those concepts of
natural language which do not fit
into the closed frame of scientific thought—for
instance, those of religion.Modem physics has in many ways increased this skepticism; but it has,
at the same time turned it against the overestimation of precise scientific
concepts, against a too-optimistic view on progress in general, and finally
against skepticism itself.The
skepticism against precise scientific concepts does not mean that
there should be a definite limitation for the
application of rational thinking.On
the contrary, one may say that
the human ability to understand may be in a certain sense
unlimited.But the existing scientific concepts cover always only
a very limited part of reality, and the other part that has not
yet been understood is infinite.Whenever
we proceed from the known into
the unknown we may hope to understand, but we may have to learn at the same
time a new meaning of the word
“understanding.” We know that any understanding must be
based finally upon the natural language because it is only there
that we can be certain to touch reality, and hence we must be skeptical
about any skepticism with regard to this natural language and its essential
concepts.Therefore, we may use these concepts as they have been used at all times.In this way modern physics
has perhaps opened the door to a wider outlook on the relation
between the human mind and reality.

This
modern science, then, penetrates in our time into other parts of the
world where the cultural tradition has been entirely different from the European civilization.There the impact of this
new activity in natural and technical science must make itself felt
even more strongly than in Europe, since changes in the conditions of life that have taken two or three centuries in Europe
will take place there within a few decades.One should expect that in many places this new activity must
appear as a decline of the older culture, as a ruthless and barbarian
attitude, that upsets the sensitive balance on which all human happiness
rests.Such consequences cannot
be avoided; they must be taken as one aspect of our time.But even there the openness of modern physics may help to some extent
to reconcile the older traditions with
the new trends of thought.For
instance, the great scientific contribution in theoretical physics that has
come from Japan since the last war may be an indication for a certain
relationship between philosophical ideas in the tradition of the Far East
and the philosophical substance of quantum theory.It may be easier to
adapt oneself to the quantum-theoretical concept of reality when
one has not gone through the naive materialistic way of thinking that still prevailed in Europe in the first decades of this
century.

Of
course such remarks should not be misunderstood as an underestimation of the damage that may be done or has been done
to old cultural traditions by the impact of technical progress.But since this whole development has for a long time passed far
beyond any control by human forces, we have to accept it as one of
the most essential features of our time and must try to connect it as much
as possible with the human values that have been
the aim of the older cultural and religious traditions.It may be allowed at
this point to quote a story from the Hasidic religion:
There was an old rabbi, a priest famous for his wisdom, to whom all people came for advice.A man visited him in despair
over all the changes that went on around him, deploring all
the harm done by so-called technical progress.“Isn’t all this technical
nuisance completely worthless,” he exclaimed “if one considers
the real values of life?” “This may be so,” the rabbi replied,
“but if one has the right attitude one can learn from everything.”
“No,” the visitor rejoined, “from such foolish things as railway or
telephone or telegraph one can learn nothing whatsoever.”
But the rabbi answered, “You are wrong.From the railway you
can learn that you may by being one instant late miss
everything.From the telegraph
you can learn that every word
counts.And from the telephone
you can learn that what we say here can be heard there.” The visitor
understood what the rabbi
meant and went away.

Finally,
modern science penetrates into those large areas of our present world in which new doctrines were established only a
few decades ago as foundations for new and powerful societies.There modern science is confronted both with the content of
the doctrines, which go back to European philosophical ideas of the
nineteenth century (Hegel and Marx), and with the phenomenon of
uncompromising belief.Since
modern physics must playa great role
in these countries because of its practical applicability, it can scarcely
be avoided that the narrowness of the doctrines is felt by those who have
really understood modern physics
and
its philosophical meaning.Therefore,
at this point an interaction between science and the general trend of
thought may
take place.Of course the
influence of science should
not be overrated; but it might be that the openness of modern science could make it easier even for larger groups of people to
see that the doctrines are possibly not so important for the society as had
been assumed before.In this
way the influence of modern science may favor an attitude of
tolerance and thereby may prove
valuable.

On
the other hand, the phenomenon of uncompromising belief
carries much more weight
than some special philosophical notions of the nineteenth century.We cannot close our eyes to the fact that the great majority
of the people can scarcely have any well-founded judgment concerning the
correctness of certain important general ideas or doctrines.Therefore, the word “belief” can for this majority not mean
“perceiving the truth of something” but can only be understood as
“taking this as the basis for
life.” One can easily understand that this second kind of
belief is much firmer, is much more fixed than the first one, that
it can persist even against immediate contradicting experience and
can therefore not be shaken by added scientific knowledge.The history of the past two decades has shown by many examples that
this second kind of belief can sometimes be upheld
to a point where it seems completely absurd, and that it then
ends only with the death of the believer.Science and history can teach us that this kind of belief
may become a great danger for
those who share it.But such
knowledge is of no avail, since one
cannot see how it could be avoided, and therefore such belief has always
belonged to the great forces in human history.From the scientific
tradition of the nineteenth century one would of course be inclined to hope that all belief
should be based on a rational
analysis of every
argument, on careful deliberation; and that this other kind of belief, in which some
real or apparent truth is
simply taken as the basis for life, should not exist.It is true that cautious deliberation based on purely rational argu­ments
can save us from many errors and dangers, since it allows readjustment
to new situations, and this may be a necessary condition for life.But
remembering our experience in modem physics it is easy to see that
there must always be a fundamental complementary between deliberation and
decision.In the practical
decisions of
life it will scarcely ever be
possible to go through all the arguments in favor of or against one
possible decision, and one will therefore always have to act on insufficient
evidence.The decision finally
takes place by pushing away all the
arguments—both
those that have been
understood and others that
might come up through further deliberation-and by cutting off all further
pondering.The decision may be
the result of deliberation,
but it is at the same time complementary to
deliberation; it excludes deliberation.Even the most important
decisions in life must always contain this inevitable element
of irrationality.The
decision itself is necessary, since there must
be something to rely upon, some principle to guide our actions.Without such a firm stand
our own actions would lose all force.Therefore, it cannot be avoided that some real or apparent truth form
the basis of life; and this fact should be acknowledged with regard to those groups of people whose basis is
different from our own.

Coming
now to a conclusion from all that has been said about modem science, one may
perhaps state that modem physics is just
one, but a very characteristic, part of a general historical
process that tends toward a unification and a widening of our present world.This process
would in itself lead to a
diminution of those cultural and political tensions that create the great
danger of our time.But it is
accompanied by another process which
acts in the opposite direction.The
fact that great masses of
people become conscious of this process of unification leads to an
instigation of all forces in the existing cultural communities that try to
ensure for their traditional values the largest possible role in the final
state of unification.Thereby
the tensions increase and
the two competing processes are so closely linked with each other
that every intensification of the unifying process-for instance,
by means of new technical progress-intensifies also the struggle for
influence in the final state, and thereby adds to the instability of the
transient state.Modern physics
plays perhaps only a small role in this dangerous process of unification.But it helps at two very
decisive points to guide the development into a calmer kind of evolution.First, it shows that the use of arms in
the process would be disastrous and, second, through its openness for all
kinds of concepts it raises the hope that in the final state
of unification many different cultural traditions may live together
and may combine different human endeavors into a new kind of balance between
thought and deed, between activity and meditation.